The acceleration versus time graph for a particle moving along a straight line is shown in the figure. If the particle starts from rest at t=0, then its speed at t=30s will be
A
20m/s
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B
0m/s
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C
−40m/s
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D
60m/s
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Solution
The correct option is C−40m/s For a−t curve, area under the graph = change in velocity.
Total area under the graph from t=0 to t=30s is given by A= Area of the graph from t=0 to t=10s + Area of the graph from t=10s to t=30s ⇒A=4×10−20×4=−40m/s Now, A=Δv (where Δv is change in velocity) ⇒−40=v30−v0 As v0=0 ∴v30=−40m/s Hence, speed of the particle at 30s=−40m/s