A particle moves in a straight line with constant acceleration 'a'. The displacements of particle from origin in times t1, t2 and t3 are s1, s2 and s3 respectively. If times are in A.P. with common difference d and displacements are in G.P. Then prove that (/51 - V53) a =
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- Traffic shock wave. An abrupt slowdown in concentrated traffic can travel as a pulse, termed a shock wave, along the line of cars, either downstream (in the traffic direction) or upstream, or it can be stationary. The figure shows a uniformly spaced line of cars moving at speed v = 27.0 m/s toward a uniformly spaced line of slow cars moving at speed vs = 5.30 m/s. Assume that each faster car adds length L = 13.0 m (car length plus buffer zone) to the line of slow cars when it joins the line, and assume it slows abruptly at the last instant. (a) For what separation distance d between the faster cars does the shock wave remain stationary? If the separation is twice that amount, what are the (b) speed and (c) direction (upstream or downstream) of the shock wave?You travel from point A to point B in a car moving at a constant speed of 70 km/h. Then you travel the same distance from point B to another point C, moving at a constant speed of 90 km/h. Is your average speed for the entire trip from A to C 80 km/h? Explain why or why not.3. The graph below shows the displacement vs time of a student leaving the NSCI 110 after physics class walking towards the cafeteria for lunch (assume a 1-D motion) At some point between NSCI 110 and the cafeteria, the student realizes they have left their cell phone in the classroom, so they turn back to get it. Displacement vs Time 120 100 nol Velocity vs Time 80 1.5 60 40 30 60 90 120 150 180 210 20 -1.5 30 60 90 120 150 180 210 Time (s) a. How far did the student walk before realizing that they left their cell phone in the classroom? How long did this take? (2 marks) b. With what velocity did the student walk back to the classroom? (2 marks) c. Fill out the velocity vs time graph above. (2 marks) Distance (m)
- NASA launches a rocket at t = is given by h(t) = - 4.912 + 349t + 318. O seconds. Its height, in meters above sea-level, as a function of time Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level.The position of an object moving along the x -axis is given by x = 5.0m 4.0 t m + 2.0 t² m. How many times does this object pass through the point x=0? A. twice, first moving in the positive x-direction, then moving in the negative x-direction B. twice, first moving in the negative x-direction, then moving in the positive x-direction C. only once, moving in the positive x-direction D. only once, moving in the negative x-direction E. neverCan I please get some help with this problem. I can't seem to figure this out. thank you!
- An object is moving in the xx-direction at 1.0 m/sm/s when it undergoes an acceleration a⃗ =0.54j^m/s2a→=0.54j^m/s2. Find its velocity vector's components after 3.6 ss.On a two-lane road, car A is traveling with a speed of 36 km/h. Two cars, B and C approach car A in opposite directions with a speed of 54 km/h each. At a certain instant when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?Q29