Question

SerCP11 2.1.P018 A race car moves such that its position fits the relationship x - (4.0 m/s)t + (0.70 m/s3)t3 where x is measured in meters and t in seconds (a) A plot of the car's position versus time is which of the following? x (m) 180 160 140 120 100 80 60 40 20 x (m) 200 180 160 140 120 100 80 60 40 20 t (s) t (s) 1.00 2.00 3.00 4.00 5.00 6.00 1.00 2.00 3.00 4.00 5.00 6.00 x (m) 25 20 15 10 x (m) 80 70. 60 50 40 30 2 1 0 t (s) 1.00 2.00 3.00 4.00 5.00 6.00 1.00 2.00 3.00 4.00 5.00 6.00 (b) Determine the instantaneous velocity of the car at t 3.4 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s. (In ord

Answer 1

(a)

Car's position versus time graph,

First graph is correct.

(b)

Given that,

x = 4t + 0.70t^3

Instantaneous velocity of car at t = 3.4 s,

v = dx / dt = d(4t + 0.70t^3) / dt

v = 4 + 2.1t^2

v = 4 + 2.1*(3.4)^2

v = 28.27 m/s

(c)

displacement during first 3.4 s,

x = 4t + 0.70t^3

x = 4*3.4 + 0.70*3.4^3 = 41.112

Average velocity during first 3.4 s,

v_avg = 41.112 / 3.4

v_avg = 12.09 m/s