Problem 2 on Motion in a Straight Line

Description:

Problem

Consider the following x − t graph.

Find,

• The average velocity during 0 s to 10 s.
• Instantaneous velocity at 2 s, 5 s, 8 s, 12 s.

Solution

We know that, average velocity is simply the ratio of total displacement and total time. Therefore,

Average velocity during 0 s to 10 s is,

Average Velocity = Total Displacement/Total Time

Average Velocity = 100/10 = 10 m/s

Instantaneous Velocity at any point is simply the slope of tangent to the curve at that point. Therefore,

At t = 2s,

Slope of Tangent = 50 - 0/2.5 - 0 = 20 m/s

At t = 5s,

Slope of Tangent = 50 - 50/7.5 - 2.5 = 0 m/s

At t = 8s,

Slope of Tangent = 100 - 50/10 - 7.5 = 20 m/s

At t = 12s,

Slope of Tangent = 0 - 100/15 - 10 = -20 m/s