The displacement of a particle moving in a straight line is given by s = t^2 − 8t + 19. Find the average vel.?
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 − 8t + 19, where t is measured in seconds.
(a) Find the average velocity over each time interval.
(i) [3, 4]
__ m/s
(ii) [3.5, 4]
__m/s
(iii) [4, 5]
__ m/s
(iv) [4, 4.5]
__ m/s
(b) Find the instantaneous velocity when t = 4.
__ m/s
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Verified answer
a)
i) Evaluate you formula at each end point of the interval, then divide by the time
elapsed during that interval:
s = t^2 − 8t + 19
s = 3^2 - 8(3) + 19 = 4
s = t^2 − 8t + 19
s = 4^2 - 8(4) + 19 = 3
3 - 4 = -1m
-1m/1sec = -1m/sec
b) Velocity is ds/dt:
s = t^2 − 8t + 19
ds/dt = 2t - 8
ds/dt = 2(4) - 8 = 0m/sec