Question

The speed-time graph for a car is shown in below figure:

(a) Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance travelled by the car during the period.
(b) Which part of the graph represents uniform motion of the car?

Answer 1

(a) Distance travelled by car in the 4 second
The area under the slope of the speed - time graph gives the distance travelled by an object.
In the given graph
56 full squares and 12 half squares come under the area slope for the time of 4 seconds.
Total number of squares $=56+\frac{12}{2}=62$ squares
The total area of the squares will give the distance travelled by the car in 4 seconds.
On the time axis, 5 squares = 2 s
$\therefore 1square=\frac{2}{5}s$
On the speed axis, 3 squares $=2m{s}^{-1}$
$\therefore 1square=\frac{2}{3}m{s}^{-1}$
$\therefore$ Area of 1 square $=\frac{2}{5}\times \frac{2}{3}=\frac{4}{15}m$
$\therefore$ Area of 62 squares $=\frac{4}{15}\times 62$
$=\frac{248}{15}=16.53m$
Therefore, car travels 16.53 m in first 4 seconds.

(b) Part MN of the graph is straight line parallel to the time axis, thus this portion of graph represents uniform motion of car.