Question

if a car goes along a straight road heading east and speeds up from 45 ft/s to 60 ft/s in 5 s, calculate the acceleration. a = 3 ft/s² n/a n e s w note: if the speed were given in miles per hour, and the time were given in minutes, you could change the minutes to a fraction of an hour and do the problem. the answer would be in miles/h².

Explanation:

Step1: Recall the acceleration formula

Acceleration \( a \) is defined as the change in velocity \( \Delta v \) divided by the time interval \( \Delta t \), so \( a=\frac{\Delta v}{\Delta t} \).

Step2: Calculate the change in velocity

The initial velocity \( v_i = 45\space ft/s \) and the final velocity \( v_f = 60\space ft/s \). So \( \Delta v=v_f - v_i=60 - 45 = 15\space ft/s \).

Step3: Calculate the acceleration

The time interval \( \Delta t = 5\space s \). Substitute \( \Delta v = 15\space ft/s \) and \( \Delta t=5\space s \) into the acceleration formula: \( a=\frac{15}{5}=3\space ft/s^2 \). Also, since the car is moving east and speeding up, the acceleration is in the same direction as the velocity, so the direction is East (E).

Answer:

\( a = 3\space \text{ft/s}^2 \) (direction: E)