Question

the velocity-time graph of a linear motion is shown below. the displacement from the origin after 8 seconds is

Answer 1

velocity is the rate of change of displacement with respect to time.

so, v = ds/dt

or, $\int{ds}=\int{v}\,dt$

means,

• displacement = area under the velocity- time graph.

so, displacement = area of first trapezium + area of 2nd trapezium

= 1/2 × [4s + (3s - 1s)] × 4 m/s + 1/2 × [(8s - 4s) + (7s - 5s)] × -2 m/s

= 1/2 × [4s + 2s] × 4m/s - 1/2 × [4s + 2s ] × 2m/s

= 6s × 2m/s - 6s × 1m/s

= 12m - 6m

= 6m

hence, displacement from the origin after 8 second is 6m

Answer 2

Answer:

Explanation:

Distance =area under the graph...

So.

Distance=[(4×1)/2]+(2×4)+[(4×1)/2]+[(-2×1)/2]+[(-2)×2]+[(-2×1)/2]

=2+8+2-1+-4+-1

=12-6

=6m

Hence the correct answer is D. 6meters.

Hope this is what you were looking for...