Everything Science Grade 10

CHAPTER 21. MOTION IN ONE DIMENSION 21.6

Example 6: Drawing avvs.tgraph from anavs.tgraph

QUESTION

The acceleration vs. time graph for a car starting from rest, is given below. Calculate

the velocity of the car and hence draw the velocity vs. time graph.

0

1

2

− 1

− 2

1 2 3 4 5 6

a(m·s−^2 )

t(s)

SOLUTION

Step 1:Calculate the velocity values by using the area under each part of the

graph.

The motion of the car can be divided into three time sections: 0 – 2

seconds; 2 – 4 seconds and 4 – 6 seconds. To be able to draw the

velocity vs. time graph, the velocity for each time section needs to be

calculated. The velocity is equal to the area of the square under the

graph:

For 0 – 2 seconds:

Area = ℓ×b

= 2s× 2 m·s−^2

= 4m·s−^1

The velocity of the car is

4 m·s−^1 at t = 2s.

For 2 – 4 seconds:

Area = ℓ×b

= 2s× 0 m·s−^2

= 0m·s−^1

The velocity of the car is

0 m·s−^1 fromt= 2s to

t= 4s.

For 4 – 6 seconds:

Area = ℓ×b

= 2s×− 2 m·s−^2

= − 4 m·s−^1

The acceleration had a

negative value, which

means that the velocity is

decreasing. It starts at a

velocity of 4 m·s−^1 and

decreases to 0 m·s−^1.

Step 2:Now use the values to draw the velocity vs. time graph.

Physics: Mechanics 423