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{ }(m)/(s^2)`

Step-by-step 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}}=(v_f-v_i)/(t_f-t_i) \\ \text{acceleration}=(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{ }(m)/(s) \\ v_i=100\text{ }(m)/(s) \end{gathered}`

replace in the formula to find a

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

therefore, the average acceleration is

`2\text{ }(m)/(s^2)`

I hope this helps you