Problem 4: Using the following data, draw a velocity-time graph for a short journey on a straight road of a motorbike.

Use the graph to calculate

• the initial acceleration    (b) the final acceleration (c) the total distance

Solution

The journey of the bike can be divided into 3 parts.

• Its velocity increases from 0 to 20 m/s in 60 sec.

It is the case of increasing acceleration. The acceleration can be found by using, vf = vi + at. Put the values,

20 = 0 + a× 60       OR        20 = 60 a          OR        a = 20/60

OR   a = 0.33 m/s      …       (1)

This equation gives the initial acceleration of the bike.

• 60 seconds onward, the bike goes with constant velocity for another 90 seconds, and therefore, the acceleration is zero during this interval of time. Therefore, a = 0      …      (2)
• Now, after 150 seconds, the bike decelerates and comes to rest after 30 seconds. Therefore, during this interval of time, vi = 20 m/s, vf = 0 m/s, t = 30 sec. To find the acceleration, we apply the equation of motion, vf = vi + at. Put the values, 0 = 20 + 30a     OR     30a = -20      OR     a = -20/30      OR     a = – 0.666 = -0.67 m/s2.     …     (3)

The negative sign shows the velocity decreases and this gives the final acceleration of the bike.

Total distance covered: The total distance the bike covers can be calculated by the three areas of the graph; 2 triangles and one rectangle. It is given by,

s = ½ (20 × 60) + (20 × 90) + ½ (30 × 20) = ½ × 1200 + 1800 + ½ × 600 = 600 + 1800 + 300 = 2700 m = 2.7 km