Acceleration - Practice Questions & MCQ

Definition: Rate of change of velocity with time.

$$
\vec{a}=\frac{\text { change in velocity }}{\text { time taken }}=\frac{\vec{v}_f-\vec{v}_i}{t}
$$

- Tips for Acceleration-
1. The body is said to have undergone acceleration if there is a change in velocity i.e., :
- Change in speed
- Change in direction
- Change in both
2. It is a vector quantity
3. Dimension $=L T^{-2}$
4. S.I unit $=m \mathrm{~s}^{-2}$

Example: A car starting from rest accelerates uniformly to a speed of $75 \mathrm{~m} / \mathrm{s}$ in 12 seconds. What is the car's acceleration?
Solution: $v_i=0$ (starting from rest)

$$
v_f=75 \mathrm{~m} / \mathrm{s}
$$

From the definition of acceleration we know that,

$$
\begin{aligned}
a & =\frac{v_f-v_i}{t} \\
& =\frac{75-0}{12}
\end{aligned}
$$
 

$$
\mathrm{a}=6.25 \mathrm{~m} / \mathrm{s}^2
$$

There are four types of acceleration
- Average acceleration- Total change in velocity per unit time taken is the average acceleration

$$
\text { Avg. acceleration }\left(\vec{a}_{a v g}\right)=\frac{\Delta \vec{v}}{\Delta t}
$$

- Instantaneous acceleration - Infinitesimal change in velocity per unit time taken is the average acceleration

$$
\text { Inst. acceleration }\left(\vec{a}_{\text {inst }}\right)=\frac{d \vec{v}}{d t}
$$