Question 2: The acceleration function of an object doing curvilinear motion is a = {(-0.2t)i+4j+1.5k} m/s², where t is in s. If its initial velocity vo = 8i m/s, and initial position is at the origin, determine the magnitude of its position when t = 3 s. (a) 25.7 m (b) 38.9 m (c) 62.3 m (d) 22.1 m
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- A car accelerates with a constant acceleration of 1.2 m · s-2 along a long straight road. How long does it take the car to accelerate from 100 kph to 110 kph, and how far does it travel while doing so? [Hint: watch your units and your significant figures. Because there is no other information, take the speeds as three significant figures.] It takes seconds to accelerate to 110 kph. While accelerating, the car travels m. Separate your answers with a comma. Example: a, ba particle initially at position r=(2j+3k)m moves to r=(2i+3j-2k)m in 2s. Find the magnitude of the particles average velocity. If the particles acceleration is a=(2i-k) m/s^2 , find the angle between the particles acceleration and displacementA computer model displays the motion of a particle on a coordinate system in real time. At time t = 0, the particle is at the origin of the coordinate system and has velocity components v₁ = 0 and "x Vy = 6.8 m/s. The particle has acceleration components of ax = -3.2 m/s² and = 0. ay (a) What are the x and y positions of the particle, in meters, at t = 4.0 s? X = y = Vx Vy m (b) What are velocity components of the particle, in m/s, at t = 4.0 s? m/s m/s = m (c) How does the speed of the particle change from t = 0 to t = 4.0 s? O The particle's speed remains constant. O The particle's speed decreases with time. O The particle's speed increases and then decreases with time. O The particle's speed increases with time.
- When chasing a hare along a flat stretch of ground, a greyhound leaps into the air at a speed of 12.1 m/s, at an angle of 27.0° above the horizontal. (a) What is the range of his leap and (b) for how much time is he in the air? (a) Number i Units (b) Number i UnitsThe coordinates of a bee flying in the xy-plane are given by x(t) = At and y(t) = C - Bt², where A = 3.2 m/s, B = 1.4 m/s², and C= 2.5 m. Calculate the velocity and acceleration vectors of the bee as a function of time. Write your answers in unit vector notation.Suppose that a particle begins its motion from the origin and meets the velocity (in m / s) given by: vx (t) = 2.50t vy (t) = 3.50√t. for t> 0 in seconds. Find the speed of the particle at t = 5.00 s What is the acceleration vector (in rectangular components) at t = 2.00 s ? Find the magnitude of the displacement between t = 0.00 s and t = 6.00 s
- Problem 4: A particle moving along a straight path has an acceleration defined by a = 0.6s + 3.6 ft/s², where s is in feet. If the particle's speed is 1.2 ft/s at s = 0, find its speed when s = 8 feet.The acceleration of an object (in m/s2) is given by the function a(t)=7sin(t)a(t)=7sin(t). The initial velocity of the object is v(0)=−1v(0)=-1 m/s. Round your answers to four decimal places. v(t) = -7cos(t) + 6 The objects displacement from time 0 to 3 is: 17.01216 meters Find the total distance traveled by the object from time 0 to time 3.An object is travelling in 1-dimension (i.e. along the x- axis) with a velocity described by the equation: v(t)=v0+1/6st^3 , where s and v0 are constants. The object’s position, and acceleration at time t = 0 are given by d0, and a0 respectively. In terms of the variables given, what is the average acceleration of the object over the interval from 0 to 2 seconds.