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An object moves along the x-axis Its coordinates is given as function of time as x = 7t - 3t² m where x is in metres and t is in seconds. Its average speed over the interval t =0 to t = 4 sec , is

An object moves along the x-axis Its coordinates is given as function
of time as x = 7t - 3t² m where x is in metres and t is in seconds. Its average speed over the interval t =0 to t = 4 sec , is 

Grade:12th pass

1 Answers

Vikas TU
14149 Points
2 years ago
Dear student 
The differentiation of displacement gives velocity.
x = 7t - 3t²
V = dx/dt
V = 7 - 6t
Plot the velocity time graph using the above equation.
2.The velocity time graph and speed time graph are similar except negative part of velocity time graph.
3.The negative part of velocity time graph becomes positive in speed time graph.
4.The total area under speed time graph gives the total distance travelled.
5.Area under the graph upto t = 4 sec , gives the distance travelled upto 4 seconds.
From the graph ,
Total distance = 169/6 m.
Total time = 4 sec
6.Average speed = total distance / time taken.
Average speed = (169/6)(1/4)
Average speed = 169/24 m/s

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