Question

1. (4 points) the figure shows a graph of the velocity of an object as a function of time. what is the acceleration of the object at the following times? (a) at 1.0 s (b) at 3.0 s 5. (3 points) which of the following is correct?

Explanation:

Step1: Recall acceleration - velocity relationship

Acceleration $a=\frac{\Delta v}{\Delta t}$, which is the slope of the velocity - time graph.

Step2: Find acceleration at $t = 1.0\ s$

In the time interval $0 - 2.0\ s$, the velocity changes from $v_0 = 0\ m/s$ to $v_1= 10\ m/s$. Using $a=\frac{\Delta v}{\Delta t}$, with $\Delta v=10 - 0=10\ m/s$ and $\Delta t = 2.0-0 = 2.0\ s$. So $a=\frac{10 - 0}{2.0-0}=5\ m/s^{2}$.

Step3: Find acceleration at $t = 3.0\ s$

In the time interval $2.0 - 4.0\ s$, the velocity is constant ($v = 10\ m/s$). Since $\Delta v=0$, then $a=\frac{0}{4.0 - 2.0}=0\ m/s^{2}$.

Answer:

(a) $5\ m/s^{2}$
(b) $0\ m/s^{2}$