Question

given the following velocity time graph, which statement best describes this objects motion?

a the object is speeding up by 10m/s every second
b the object is slowing down by 10m/s every second
c the object is moving 10 meters every second
d the object is at rest

Explanation:

Step1: Recall the formula for acceleration

Acceleration \(a=\frac{\Delta v}{\Delta t}\).

Step2: Calculate the change in velocity \(\Delta v\) and time \(\Delta t\)

At \(t = 0\), \(v_0=0\ m/s\); at \(t = 5\ s\), \(v = 50\ m/s\). So \(\Delta v=v - v_0=50 - 0=50\ m/s\), \(\Delta t = 5-0 = 5\ s\).

Step3: Calculate the acceleration

\(a=\frac{\Delta v}{\Delta t}=\frac{50}{5}=10\ m/s^{2}\). Since the acceleration is positive and velocity is increasing with time.

Answer:

A. The object is speeding up by 10m/s every second