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Q.

The speed-time graph of a vehicle is shown here.

Find how far the vehicle travels in the first 4 seconds

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a

60 m

b

11.3 m

c

16.8 m

d

12.7 m

answer is C.

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Detailed Solution

The vehicle travels

16.8 m

in first

4

seconds.
The distance travelled by the vehicle in the first 4 seconds is given by the area between the
Speed-time curve and the time axis from

t = 0

to

t = 4 s

.

Question Image

In order to find the distance travelled by the vehicle in the first

4

seconds, we have to count the number of squares in the shaded part of the graph. While counting the number of shaded squares of the graph, the squares which are half or more than half are counted as one square but the squares which are less than half are not counted. So, the total number of squares in the shaded part of the graph is found to be

63

.
To calculate the distance represented by 1 square of the graph, look at the X-axis, we find that

5

squares on the

X - axis

represent a time of 2 seconds.

5

squares on

X - axis

= 2 s

Therefore

1

square on

X - axis = 2 / 5 s

Squares on

Y - axis

represent a speed of

2 m / s

.

3

squares on

Y - axis = 2 m / s

Therefore

1

square on

Y - axis = \frac{2}{3} m / s

Now Area (distance)

= \frac{2}{5 s} \times \frac{2}{3} m / s

\Rightarrow = \frac{4}{15} m

So

1

square represents distance

= \frac{4}{15} m

For

63

squares represent distance

= \frac{4}{15} \times 63

\Rightarrow = 16.8 m

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