Question

At t = 0, a car has a speed of 100m/s. At t = 25s, its speed is 150 m/s. What is its average acceleration during this time interval?

Answer 1

$2\text{ }\frac{m}{s^2}$

Explanation

Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), it can be represented by

$\begin{gathered} \text{acceleration}=\text{ }\frac{\text{change in sp}eed}{\text{time to do that}}=\frac{v_f-v_i}{t_f-t_i} \\ \text{acceleration}=\frac{v_f-v_i}{t_f-t_i} \\ \text{where} \\ v_fis\text{ the final sp}eed \\ v_iis\text{ the Initial sp}eed \\ t_fis\text{ the final time} \\ t_{i\text{ }}is\text{ the initial time} \end{gathered}$

then

Step 1

let

$\begin{gathered} t_i=0 \\ t_2=25\text{ s} \\ v_f=150\text{ }\frac{m}{s} \\ v_i=100\text{ }\frac{m}{s} \end{gathered}$

replace in the formula to find a

$\begin{gathered} \text{acceleration}=\frac{v_f-v_i}{t_f-t_i} \\ a=\frac{(150-100)\frac{m}{s}}{(25-0)s} \\ a=\frac{50\frac{m}{s}}{25s} \\ a=2\text{ }\frac{m}{s^2} \end{gathered}$

therefore, the average acceleration is

$2\text{ }\frac{m}{s^2}$

I hope this helps you