Motion in a Straight Line

A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s ?

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in \(15\) \(s\) and (ii) the time at which the car will catch up with the scooter are, res...

An automobile, travelling at \(40\,\) km/h, can be stopped at a distance of \(40\,\) m by applying brakes. If the same automobile is travelling at \(80\,\) km/h, the minimum stopping distance, in metres, is (assume no skidding) :

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s2 and the car has acceleration 4 m/s2 . The car will catch up wit...

Which graph corresponds to an object moving with a constant negative
acceleration and a positive velocity ?

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs
time?

Two stones are thrown up simultaneously from the edge of a cliff \(240\) \(m\) high with initial speed of \(10\) \(m/s\) and \(40\) \(m/s\) respectively. Which of the following graph best represents the time variation of relative position o...

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the
particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation
between H, u and n is:

An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by :
\({{dv} \over {dt}} = - 2.5\sqrt v\) where v is the instantaneous speed. The time taken by the object, to come to rest, would be :

Consider a rubber ball freely falling from a height \(h=4.9\) \(m\) onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic.
Then the velocity as a function ...

A body is at rest at \(x=0.\) At \(t=0,\) it starts moving in the positive \(x\)-direction with a constant acceleration. At the same instant another body passes through \(x=0\) moving in the positive \(x\) direction with a constant speed. T...

The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity
'v' that varies as \(v = \alpha \sqrt x\). The displacement of the particle varies with time as

A parachutist after bailing out falls \(50\) \(m\) without friction. When parachute opens, it decelerates at \(2\,\,m/{s^2}.\) He reaches the ground with a speed of \(3\) \(m/s\). At what height, did he bail out?

The relation between time t and distance x is t = ax2 + bx where a and b are constants.
The acceleration is

A car starting from rest accelerates at the rate f through a distance S, then continues
at constant speed for time t and then decelerates at the rate \({f \over 2}\) to come to rest. If the
total distance traversed is 15 S, then

An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m.
If the car is going twice as fast, i.e 120 km/h, the stopping distance will be

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the
ground. What is the position of the ball in \({T \over 3}\) seconds?

The co-ordinates of a moving particle at any time 't' are given by x = \(\alpha\)t3 and y = βt3. The speed to the particle at time 't' is given by

A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the
same car is moving at a speed of 100 km/hr, the minimum stopping distance is

Speeds of two identical cars are \(u\) and \(4\)\(u\) at the specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is :

From a building two balls A and B are thrown such that A is thrown upwards and B downwards ( both vertically with the same speed ). If vA and vB are their respective velocities on reaching the ground, then