Question

The speed-time graph for a car is shown is Fig. 8.12.
(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

According to the given speed-time graph, we are asked to solve the below mentioned questions:

Knowledge required:

• In the velocity time graph / speed time graph the distance or displacement can be founded by the area under the curve!

Required solution:

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.

• Refer to 1st attachment

$:\implies \sf Distance \: = Area \: under \: curve \\ \\ :\implies \sf s \: = Area \: under \: curve \\ \\ :\implies \sf s \: = Area \: of \: triangle \\ \\ :\implies \sf s \: = \dfrac{1}{2} \: Base \times Height \\ \\ :\implies \sf s \: = \dfrac{1}{2} \times (4-0) \times (6-0) \\ \\ :\implies \sf s \: = \dfrac{1}{2} \times 4 \times 6 \\ \\ :\implies \sf s \: = \dfrac{1}{2} \times 24 \\ \\ :\implies \sf s \: = 12 \: m \\ \\ :\implies \sf Distance \: = 12 \: m$

b) Which part of the graph represents uniform motion of the car?

• Refer for attachment 2nd

The underlined blue portion of the graph from 6 seconds to further shows the graph represents uniform motion of the car where the car is moving with an uniform speed that is equal velocity in equal interval of time.

Additional information:

↪️ A v-t graph parallel to x axis, represents, uniform motion of a body that have a constant speed

↪️ The slope of D-T graph gives the _____ of the object in motion.

• The slope of Distance Time or Displacement Time graph give the speed of the object in motion.

↪️ Distance or displacement are same in the matter of graphs in motion

↪️ Speed and velocity are same in the matter of graphs in motion

↪️ The slope of V-T graph gives the _____ of the object in motion.

• The slope of Velocity Time graph give the acceleration of the object in motion.

↪️ The area under curve of V-T graph gives the _____ of the object in motion.

• The area under curve of Velocity Time graph gives the distance/displacement of the object in motion.