Introduction to acceleration

Q. The displacement of a body in $8\text{s}$, starting from rest, with an acceleration of $20{\text{cm/s}}^2$ is

1. $64\text{m}$
2. $64\text{cm}$
3. $640\text{cm}$
4. $0.064\text{m}$

Q. For uniformly accelerated motion, both magnitude and of acceleration must remain constant.

1. strength
2. direction
3. speed

Q. A vehicle can accelerate or decelerate at a maximum value of $1m{s}^{-2}$ and can attain a maximum speed of $20m{s}^{-1}$. If it starts from rest, what is the shortest time in which it can travel $1000m$, in a straight path, if it has to come to rest at the end of $1000m$?

1. $50s$
2. $70s$
3. $30s$
4. $20s$

Q.

If a body starts from rest to the motion, its

1. $u=0$

2. $a=0$

3. velocity increases

4. velocity decreases

Q. A body is moving along a straight line. Its velocity-time graph is as shown. Choose the correct option.

1. Displacement and distance covered by body are same.
2. Initially motion is retarded, then accelerated.
3. Average speed is zero.
4. Initially, particle is moving towards origin and then away from origin.

Q. A car is speeding at $90$ km/h in a restricted speed area. A police jeep starts from rest just as the speeder passes it and accelerates at a constant rate of $5{\text{m/s}}^2$. Velocity of police jeep when it catches up with the speeder's car will be

Q. The displacement of a body in $8\text{s}$, starting from rest, with an acceleration of $20{\text{cm/s}}^2$ is

1. $64\text{m}$
2. $64\text{cm}$
3. $640\text{cm}$
4. $0.064\text{m}$

Q. The retardation experienced by a moving motor boat after its engine is cut off, is given by $\frac{dv}{dt}=-8v^2$. If the magnitude of velocity at cut off is $v_0=3\text{m/s}$, the magnitude of the velocity $1\text{sec}$ after the cut off is (in $\text{m/s}$)

1. $\frac{3}{25}$
2. $\frac{24}{25}$
3. $\frac{1}{8}$
4. $\frac{3}{28}$

Q. The acceleration-displacement graph of a partice moving in a straight line is shown in the figure. Initial velocity of the particle is zero. Find the velocity of the particle when displacement of the particle is $12\text{m}$.

1. $3\sqrt{2}\text{m/s}$
2. $2\sqrt{5}\text{m/s}$
3. $4\text{m/s}$
4. $4\sqrt{3}\text{m/s}$

Q.

Give reason:

(b) An athlete always runs some distance before taking a jump.

Q. A particle with uniform retardation along a straight line distances $a$ and $b$ in successive intervals $p$ and $q$ seconds. The acceleration of the particle is

1. $\frac{2(aq-bp)}{pq(p+q)}$
2. $\frac{2(bp-aq)}{q(p+q)}$
3. $\frac{2(aq+bp)}{pq(p+q)}$
4. $\frac{2(aq-bp)}{pq(p-q)}$

Q. If velocity of a particle is given by $v=2t-1$, then find the acceleration of particle at $t=2s$.

1. $2{\text{m/s}}^2$
2. $4{\text{m/s}}^2$
3. $8{\text{m/s}}^2$
4. $6{\text{m/s}}^2$

Q. On seeing a speed limit road sign, you apply brakes that bring your car from the speed of $30\text{m/s}$ to a speed of $20\text{m/s}$, covering a distance of $100\text{m}$ at a constant deceleration. How much time is required for the given decrease in speed?

1. $3\text{s}$
2. $4\text{s}$
3. $2\text{s}$
4. $5\text{s}$

Q. If a particle moves with a constant velocity,

1. Its acceleration is positive
2. Its acceleration is negative
3. Its acceleration is zero
4. Its speed is zero

Q.

If the velocity-time graph looks like this,

then acceleration is .

1. increasing
2. constant
3. zero

Q. The displacement of a particle varies with time $t$ as: $s=\alpha t^2-\beta t^3$. Determine the time $\left(t\right)$ at which acceleration of the particle becomes $0$.

1. $\frac{\alpha }{3\beta }$
2. $\frac{\alpha }{\beta }$
3. $\frac{3\beta }{\alpha }$
4. $\frac{2\alpha }{3\beta }$

Q. What is the acceleration, if the body starts from the rest and travels a distance of $s\text{m}$ in $2$ seconds?

1. $\frac{2}{3}s{\text{m/s}}^2$
2. $\frac{3}{2}s{\text{m/s}}^2$
3. $\frac{1}{3}s{\text{m/s}}^2$
4. $\frac{1}{2}s{\text{m/s}}^2$

Q. 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 rate $\frac{f}{2}$ to come to rest. If the total distance covered is $15s$, then which one is correct?

1. $s=\frac{f{t}^2}{72}$
2. $s=\frac{f{t}^2}{4}$
3. $s=\frac{f{t}^2}{6}$
4. $s=\frac{f{t}^2}{2}$

Q. A man loses $20\%$ of his velocity after running through $108\text{m}$. If the rate by which he is losing his velocity remains constant, what is the maximum distance he will cover?

1. $218\text{m}$
2. $300\text{m}$
3. $324\text{m}$
4. $192\text{m}$

Q. If the velocity time graph is some straight line parallel to the x axis, then definitely, velocity isand acceleration is.

1. constant
2. varying
3. zero
4. constant

Q. Assertion : A positive acceleration of a body can be associated with a ‘slowing down’ of the body.
Reason : Acceleration is a vector quantity.

1. If both assertion and reason are true and the reason is the correct explanation of the assertion.
2. If both assertion and reason are true but reason is not the correct explanation of the assertion.
3. If assertion is true but reason is false.
4. If the assertion and reason both are false.
5. If assertion is false but reason is true.

Q. Velocity - displacement graph of a particle moving in a straight line is as shown in figure

1. magnitude of acceleration of particle is decreasing
2. magnitude of acceleration of particle is increasing
3. acceleration versus displacement graph is straight line
4. acceleration versus displacement graph is parabola

Q. A body starts from orgin and moves along x-axis such that its velocity is $v=(4t^3-2t)$ m/s. Acceleration of particle when it is 2 m from origin is.

1. $10m/s^2$
2. $20m/s^2$
3. $11m/s^2$
4. $22m/s^2$

Q. The displacement ($s$) of a particle is proportional to the first power of time $t$, i.e., $s\propto t$; then the acceleration of the particle is

1. Infinite
2. Zero
3. A small finite value
4. A large finite value

Q. Assertion: A body can have an acceleration even if its velocity is zero at a given instant of time.
Reason: A body is momentarily at rest when it reverses its direction of motion.

1. If both assertion and reason are true and the reason is correct explanation of the assertion
2. If both assertion and reason are true, but reason is not correct explanation of the assertion
3. The assertion is true, but the reason is false
4. The assertion is false and reason is true

Q. An object moves velocity $\overrightarrow{v}$ having constant accelaration $\overrightarrow{a}$. Which of the following expressions are variable quantities ?

1. $\frac{d|\overrightarrow{v}|}{dt}$
2. $\left|\frac{d\overrightarrow{v}}{dt}\right|$
3. $\frac{d\left(|\overrightarrow{v}{|}^2\right)}{dt}$
4. $\frac{d\left(\frac{\overrightarrow{v}}{\overrightarrow{|v|}}\right)}{dt}$