# A particle P moves in a straight line. Its displacement from the origin O is given by

Chapter 17, Problem 7

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QUESTION:

A particle P moves in a straight line. Its displacement from the origin O is given by s(t) = 100t + 200e t 5 cm where t is the time in seconds, t > 0. a Find the velocity and acceleration functions. b Find the initial position, velocity, and acceleration of P. c Discuss the velocity of P as t ! 1. d Sketch the graph of the velocity function. e Find when the velocity of P is 80 cm per second.

Step 1 of 4

The displacement equation is given as.

For determining the velocity of the particle P, differentiate the displacement equation with respect to .

Hence the velocity of the particle P is .

For determining the acceleration of the particle P, differentiate the velocity equation with respect to  .

Hence the velocity of the particle P is  .

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