Question

1. a car takes 10 seconds to go from rest to 25 miles per hour at constant acceleration. determine the acceleration of the car and its displacement.

Explanation:

Step1: Convert speed to SI units

First, convert 25 miles per hour to meters per second. 1 mile = 1609.34 meters and 1 hour = 3600 seconds. So, $v = 25\times\frac{1609.34}{3600}\ m/s\approx11.18\ m/s$. The initial velocity $u = 0\ m/s$ and time $t = 10\ s$.

Step2: Calculate acceleration

Use the formula $a=\frac{v - u}{t}$. Substitute $u = 0\ m/s$, $v\approx11.18\ m/s$ and $t = 10\ s$ into the formula. So, $a=\frac{11.18 - 0}{10}=1.118\ m/s^{2}$.

Step3: Calculate displacement

Use the formula $s=ut+\frac{1}{2}at^{2}$. Since $u = 0\ m/s$, the formula simplifies to $s=\frac{1}{2}\times1.118\times10^{2}=55.9\ m$.

Answer:

Acceleration: $1.118\ m/s^{2}$, Displacement: $55.9\ m$