Equation of motion

Q.

An electron moving with a velocity of $5\times {10}^4{\mathrm{ms}}^{-1}$ enters into a uniform electric field and acquires a uniform acceleration of ${10}^4{\mathrm{ms}}^{-2}$ in the direction of its initial motion

(i) Calculate the time in which the electron would acquire a velocity double of its initial velocity.

(ii) How much distance the electron would cover in this time?

Q.

A ball thrown up vertically returns to the thrower after $6s$. Find (i) velocity (ii) Maximum height it reaches (iii) Position after $4s$

Q.

A ball is thrown vertically upwards with a velocity of $49m/s$. Calculate the total time it takes to return to the surface of the earth.

Q.

What is the dimensional formula of acceleration?

Q.

A car is travelling at 15 m/s. If its velocity increases to 20 m/s in 5 s then find the acceleration of the car.

Q.

A ball thrown vertically upward rises to a height of $20m$. If the acceleration due to gravity is $10m{s}^{-2}$, calculate the time taken to gain the maximum height?

Q. A ball is thrown upwards with a velocity of $10m{s}^{-1}$. Find the maximum height reached by the ball.

1. $13m$
2. $5m$
3. $15m$
4. $16m$

Q. Raj standing on the edge of a cliff of height 35 m above the ground throws the first ball straight up with an initial velocity of 30 $\frac{m}{s}$, and then throws the second ball straight down with the same initial velocity 30 $\frac{m}{s}$. What are their respective velocities just before they hit the ground. (Take a = 10 $m/s^2$)

1. $9\sqrt{2}$ $\frac{m}{s}$, $9\sqrt{2}$ $\frac{m}{s}$
2. $16\sqrt{2}$ $\frac{m}{s}$, $16\sqrt{2}$ $\frac{m}{s}$
3. 18 $\frac{m}{s}$, 18 $\frac{m}{s}$
4. 40 $\frac{m}{s}$, 40 $\frac{m}{s}$

Q.

An object is thrown vertically upwards to a height of $10\mathrm{m}$. Calculate its time taken by the object to reach the highest point.

Q. A car decreases its speed from $80kmh{r}^{-1}$ to $60kmh{r}^{-1}$ in $5$ seconds. The acceleration of the car is:

1. $-1.11m{s}^{-2}$
2. $1.11m{s}^{-2}$
3. $-1.62m{s}^{-2}$
4. $1.62m{s}^{-2}$

Q.

An express train going towards Delhi is travelling at a speed of $90kmph$. Brakes are applied so as to produce a uniform acceleration of $–0.5m{s}^{-2}$ . Find how far the train will go before it is brought to rest.

1. $600m$

2. $725m$

3. $625m$

4. $500m$

Q. Question 22(ii)
An electron moving with a velocity of $5\times {10}^{4}m{s}^{-1}$ enters into a uniform electric field and acquires a uniform acceleration of ${10}^{4}m{s}^{-2}$ n the direction of its initial motion.

(ii) How much distance the electron would cover in this time?

Q. A ball is thrown upwards with an initial velocity of $20m{s}^{-1}$. Find the time of flight and the maximum height reached by the body respectively. ($g=10m{s}^{-2}$)

1. $4s$
   $20m$
2. $5s$
   $25m$
3. $4s$
   $24m$
4. $5s$
   $30m$

Q. A toy car accelerates from rest at $2m{s}^{-2}$ for 3 seconds. Afterwards the car begins to slow down. It travels a combined total of 27 meters before coming to rest. What is its rate of acceleration when stopping and what is the total time of the motion?

1. $a=-2m{s}^{-2},t=6s$
2. $a=-1m{s}^{-2},t=9s$
3. $a=-2m{s}^{-2},t=9s$
4. $a=-1m{s}^{-2},t=6s$

Q. A car decreases its speed from $80kmh{r}^{-1}$ to $60kmh{r}^{-1}$ in $5$ seconds. The acceleration of the car is:

1. $-1.62m{s}^{-2}$
2. $1.62m{s}^{-2}$
3. $-1.11m{s}^{-2}$
4. $1.11m{s}^{-2}$

Q.

A stone is thrown in a vertically upward direction with a velocity of 5 m/s. If the acceleration of the stone during its motion is 10 m/s² in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?