A race car moves such that its position fits the relationshlp x-(6.0 m/se+ (0.90

Question

A race car moves such that its position fits the relationshlp x-(6.0 m/se+ (0.90 myshe where x is measured in meters and t In seconds. (a) A plot of the r's position versus time is which of the following? x (m) 240 200 x (m) 10 100 90 140 120- 100 60 50 40 30 20 3.00 2.00 3.00 4.00 500 00 O 1.00 2.00 3.00 4.00 5.00 6.00 t (s) X(m) x (m) 35 30 25 20 .00 2.00 3.00 4.00 5.00 6.00 100 2.00 3.00 4.00 5.00 6.00 r (s) (b) Determine the instantaneous velocity of the car at t 4.7s, using in your answer.) using time intervals of 0.40 s, 0.20 s, and 0.10 s. (In order to better see the limiting process keep at lea At 0.40 s m/s (Use the interval from t-4.50 s to 4.90 s) m/s (Use the interval from t4.60 s to 4.80 s.) m/s (Use the interval from t4.65 s to 4.75 s.) -0.20 s -0.10 s

Explanation / Answer

a) x = 6t + .9t3

At t = 6s, x = 230.4m and that fits the criterion of the 1st graph only. So option a.

b) t = 4.5 to 4.9

x = 109.01 to 135.28

v1 = 65.68m/s

t = 4.6 to 4.8

x = 115.20 to 128.33

v2 = 65.66m/s

t = 4.65 to 4.75

x = 118.39 to 124.95

v3 = 65.65m/s

c) Using Calculus we get

vavg  at t = 4.7s = dx/dt = 6 + 2.7t2 =  6 + 2.7 * (4.7)2 = 65.64m/s

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