Question

fill in the blank question a runner traveling at 8 m/s begins to slow down by accelerating at -1 m/s² for 4 seconds. without the acceleration, the runner would have ran \boxed{} m during those 4 seconds, but the acceleration reduced the distance by \boxed{} m.

Explanation:

Step1: Calculate distance without acceleration

Distance = speed × time
$d_1 = 8 \times 4 = 32$ m

Step2: Calculate distance with acceleration

Use kinematic equation $d = v_0 t + \frac{1}{2} a t^2$
$d_2 = 8 \times 4 + \frac{1}{2} \times (-1) \times 4^2 = 32 - 8 = 24$ m

Step3: Calculate distance reduction

Subtract the two distances
$\Delta d = d_1 - d_2 = 32 - 24 = 8$ m

Answer:

Without acceleration: 32 m; Distance reduced by: 8 m