Consider the case of a student wishing to investigate the acceleration of a small cart in a lab exercise. The students makes the following measurements of the cart's velocity at the specified times. The equation that relates velocity, acceleration, and time is given by: v=v0 +at. The measurements of velocity and time are: Time 0.40 sec 1.00 sec 1.85 sec 2.51 sec 3.05 sec 3.92 sec Velocity 14.29 cm/s 15.87cm/s 18.13cm/s 21.04cm/s 21.35cm/s 24.42cm/s Plot velocity versus time. Determine the best fit line and the y-intercept. Use these findings from the graph and Equation 17 to determine the initial velocity, v0, and the acceleration, a. v0 = __________________ a = ___________________

Q: Position (cm) Elapsed Time (ms) 0. 0. 20 237 40 325 60 409 80 469 520 100

A: The positive X-axis represents the position and the positive Y-axis represents the elapsed time. The…

Q: student holds a ball 1.55 meters above the ground and drops it. Her friend uses a stopwatch and…

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Q: The velocity versus time graph for a golf ball struck from the ground is shown in the graph below.…

A: From 2 to 2.5 s, the slope of the graph is negative and from 2.5 to 5 s, the slope of the graph is…

Q: When a clock reads 4.0 seconds a cart's velocity in the positive x direction is 6m/s When the clock…

A: The initial velocity of the cart is 6 m/s at 4 s.The final velocity of the cart is 10 m/s at 6 s.

Q: Based on the velocity and time graph given  how far does the object move in the interval from t=0…

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Q: A student holds a ball 1.55 meters above the ground and drops it. Her friend uses a stopwatch and…

A: We have been given that h = 1.55 m t = 0.57 Using these values, the value of acceleration due to…

Q: 8. From the slope of the best-fit line, determine the average acceleration. Record this information…

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Q: Shown below is a graph of velocity versus time for a moving object. The object starts at position x…

A: Given Data:  Initial position of object x=0 m Final time t=2 s At t=2 s, velocity (v)= 10 ms

Q: A spaceship is traveling at a velocity of v0 = (37.3 m/s)i when its rockets fire, giving it an…

A: Data Given ,  Initial velocity ( V0 ) = ( 37.3 i ) m/s Acceleration ( a ) = ( 2.55 i + 4.19 k ) m/s2…

Q: 8. From the slope of the best-fit line, determine the average acceleration. Record this information…

A: From best fit line, at t= 0s , v = 0cm/s and at t= 0.15s , v = 133.33 cm/s Slope of best fit line =…

Q: An object moves in along the x-axis with an acceleration given by: a = 5t2 + 10t (m/s2). The…

A: Consider the expression of the acceleration. Using the definition of acceleration. Integrating…

Q: Using the given graph, how do you calculate for the time constant (s) if the equation is given by…

A: From the curve we see that at time t = 10s the value of current is around, i(t)= 2.5 × 10-6 A.…

Q: A plot of velocity versus time for a car for the first 15 seconds of motion is shown in the diagram…

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Q: An object is moving east at 15 m/s and another object Is moving south at 15 m/s. Which of the…

A: One object is moving towards east with speed 15 m/s and other is moving towards south with speed 15…

Q: A. C D -2 0 5 15 25 35 45 55 65 75 85 95 105 115 Time (s) 21. Sketch the acceleration vs time graph…

A: Acceleration is the rate of change of the velocity of the object with respect to time. a = ∆v/∆t…

Q: car travels in the +x-direction on a straight and level road. For the first 4 of its motion, the…

A: Given average velocity vav = 6.25 m/s Time taken t = 4 sec

Q: 80p 60

A: Slope of velocity time graph represent acceleration.

Q: The acceleration of a crate sliding down a ramp is given by ax = (0.25t2) m/s? and ay = (1.5t) m/s?,…

A: Given data :  Crate acceleration : ax = (0.25t2) m/s2  and  ay = (1.5t3) m/s2  At t= 0, vx = 3 m/s…

Q: An object moves along a straight line and experiences a constant acceleration of +1.53 cm/s2. At t =…

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Q: v (m/s) 50 45 40 35 30 25 20 15 10 5 0 2 4 6 8 10 12 14 1 (s)

A: In this question the velocity time graph is showing the velocity of a motorcycle police officer   In…

Q: The figure shows a graph of the velocity of an object as a function of time. What is the…

A: Acceleration = 20/2 = 10  ms-2  Equation  x = ut + (1/2)at2 x = 0×t + (1/2)at2 x = (1/2)at2  x =…

Q: The acceleration of a rocket is a = -bV, where V is the speed of exhaust gases coming out of the…

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Q: he velocity vx (in m/s) of an object is given by the equation vx = 4t + 3, where t is the time in…

A: Equation of velocity of object is; vx=4t+3 Part A: Displacement of object is calculated by…

Q: Consider a toy rocket that undergoes one dimensional motion. It is launched from rest straight up…

A: Given:- ∆t1= time taken to go from o to A a= acceleration of rocket before t1 = acceleration of…

Q: A hot air balloon is moving vertically upwards at a constant rate of 9.0 m/s. As the balloon rises,…

A: We have been given that the balloon is moving at 9.0 m/s in the positive z-direction. It drops a…

Q: Consider a toy rocket that undergoes one dimensional motion. It is launched from rest straight up…

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Q: what is the magnitude of the acceleration for an object starts with velocity ( 2i + 3j) m/s and…

A: Initial velocity of the object u→=2i^+3j^ (m/s) and final velocity of the object v→=13i^+7j^ (m/s),…

Q: An object moving due to gravity can be described by the motion equation y = yo + vot –gt?, where t…

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Q: An object has the acceleration graph shown. Its velocity at t = 0 s is νx = 2.0 m/s. Draw the…

A: The acceleration time graph is given, and at t= 0s the initial velocity vx = u= 2 m/s. Now at t=0s,…

Q: The position of a moving object was measured and furious times and the results are shown in the…

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Q: A car is waiting at an intersection. When the traffic light turns green, the car starts moving.…

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Q: Pedro   who  is  on  top  of  a roof  of  a  high  building  drops  a  piece  of  metallic material.…

A: Solution:           for the second object using                   v² = u ² + 2as2 where          v =…

Q: Starting at x = - 17 m at time t = 0 s, an object takes 17 s to travel 55 m in the +x direction at a…

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Q: A particle moves at 82 m/s when subjected to an acceleration of A = −t2/4−t2/4 m/s2. How far in…

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Q: An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground.…

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Q: A student holds a ball 1.55 meters above the ground and drops it. Her friend uses a stopwatch and…

A: Given: height of the ball above the ground (y) = 1.55 m            time taken by the ball to hit the…

Q: The next few questions challenge you to figure out the acceleration due to gravity ( g ) on various…

A: Solution:-                   Using 2nd equation of motion;…

Q: An object is dropped in an unknown planet from height 50 m, it reaches the ground in 2 s . The…

A: Solution: Given: An object is dropped in an unknown planet from height 50 m, it reaches the ground…

Q: The following conversions occur frequently in physics and are very useful. Use and to convert 60 mph

A: Miles per hour and feet per second are the units of speed, these units are used to measure speeds.…

Q: Position Vs Time 4500.0 Position Vs Time 8500.0 Time (s) Position (m) 0.0 0.0 3000.0 10.0 252 2500.0…

A: To determine average acceleration we observe how the curve changes with time as seen in figure the…

Distance and Speed

The speed, distance and time relation forms the basis of study of motion. You will need these concepts in the study of Mechanics. This concept is applicable for students who are studying the following courses –