Embibe Experts Solutions for Exercise 1: SAT 2019

Suppose that the acceleration versus time graph of a particle that starts from rest at $t=0$ is as shown in the figure. 

At what instant does the particle come to rest for the first time?

Suppose that the acceleration versus time graph of a particle that starts from rest at $\mathrm{t}=0$ is as shown in the figure.

What is the total distance travelled by the particle during $30 \mathrm{s}$?

Two identical objects A and B each of mass m start moving along the same vertical line in opposite directions at the same instant. Object A is dropped from rest from a height H above the ground and object B is projected vertically upward from the ground with speed $\mathrm{u}=\sqrt{2\mathrm{gH}}$. At what height above the ground do they collide?

Two identical objects A and B each of mass m start moving along the same vertical line in opposite directions at the same instant. Object A is dropped from rest from a height H above the ground and object B is projected vertically upward from the ground with speed $\mathrm{u}=\sqrt{2\mathrm{gH}}$. After they collide, they stick to each other. What is the loss in their total energy?

Figures given below show velocity – time curves for a moving object. Identify the one which may be realised in practice.

A ball is thrown vertically upwards at a speed $\mathrm{u}$ and returns to the thrower. There are two instants at which the ball has equal kinetic and potential energies. The difference between these two instants is  

A car P is moving with a uniform speed $72 \mathrm{km} {\mathrm{hr}}^{-1}$ towards another car Q at rest on a straight level road. At a particular instance when the distance between P and Q is $525 \mathrm{m}$ the car Q started accelerating at $2 {\mathrm{ms}}^{-2}$ towards P. Find the distance travelled by Q, when both the cars meet.

A body travels the distance $AB=l$ with a speed $2 {\mathrm{ms}}^{-1}$. Thereafter, it travels $BC=l\text{'}$with speed $1.5 {\mathrm{ms}}^{-1}$ and the remaining $CC\text{'}=\left(l-l\text{'}\right)$ with $0.5 {\mathrm{ms}}^{-1}$. Calculate the average speed for this journey assuming that the body takes the same time in travelling distances $BC$ and $CC\text{'}$ .