Question

1. a baseball players motion is shown in the table below. determine if the player has a positive or negative acceleration and if they are speeding up or slowing down.

time 0.5 sec 1.0 sec 1.5 sec 2.0 sec
velocity 1.5 m/s 2.5 m/s 3.5 m/s 4.5 m/s
negative acceleration, speeding up
negative acceleration, slowing down
positive acceleration, speeding up
positive acceleration, slowing down

Explanation:

Step1: Recall acceleration - velocity relationship

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v = v_f - v_i$ and $\Delta t=t_f - t_i$. If $v_f>v_i$ (velocity is increasing), acceleration is positive and the object is speeding up. If $v_f < v_i$ (velocity is decreasing), acceleration is negative and the object is slowing down.

Step2: Analyze the velocity - time data

We have velocity values at different times: $v(0.5\ s)=1.5\ m/s$, $v(1.0\ s)=2.5\ m/s$, $v(1.5\ s)=3.5\ m/s$, $v(2.0\ s)=4.5\ m/s$. As time increases from $t = 0.5\ s$ to $t=2.0\ s$, the velocity values are increasing ($1.5\ m/s<2.5\ m/s<3.5\ m/s<4.5\ m/s$).

Answer:

positive acceleration, speeding up