Questions in Motion in A Straight Line

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A student is standing at a distance of 50 metres from the bus. As soon as the bus begins its motion with an acceleration of $1ms^{-2}$ the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is
A body A moves with a uniform acceleration \[a\] and zero initial velocity. Another body B, starts from the same point moves in the same direction with a constant velocity \[v\]. The two bodies meet after a time \[t\]. The value of \[t\] is
A particle moves along X-axis in such a way that its coordinate X varies with time \[t\] according to the equation \[x = (2 - 5t + 6{t^2})\,m\]. The initial velocity of the particle is
A car starts from rest and moves with uniform acceleration a on a straight road from time t = 0 to t = T. After that, a constant deceleration brings it to rest. In this process the average speed of the car is
An object accelerates from rest to a velocity 27.5 m/s in 10 sec then find distance covered by object in next 10 sec
If the velocity of a particle is given by \[v = {(180 - 16x)^{1/2}}\] m/s, then its acceleration will be
The displacement of a particle is proportional to the cube of time elapsed. How does the acceleration of the particle depends on time obtained
Starting from rest, acceleration of a particle is \[a = 2(t - 1).\] The velocity of the particle at \[t = 5s\] is
A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in next 5 sec. Its initial velocity will be
Speed of two identical cars are \[u\] and \[4u\] at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is

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