2. A truck driver slams on the brakes and goes 100 m in 4 s while slowing down a

Question

2. A truck driver slams on the brakes and goes 100 m in 4 s while slowing down at a constant rate coming to rest. a) Draw a picture of the process, indicate your coordinate axis, positive direction and origin. b) Write down a general formula for x(t) for the truck using your picture. Use the information given and your formula for x(t) to obtain an equation with 2 unknowns. What are the 2 unknowns? (write the symbols.) c) Write down a formula for the truck's velocity as a function of time, v(t). Use the information given in the problem to obtain a 2nd equation with the 2 unknowns (what's the truck's velocity after 4s?). d) Use algebra to solve for the initial velocity of the truck (was he speeding?).

Explanation / Answer

2] Final velocity = v = 0 m/s

t = 4s and S = 100 m

use, S = ut + (1/2)at2

100 = 4u + (1/2)a42

=> 100 = 4u + 8a

also, using v = u + at

0 = u + 4a

=> u = - 4a

therefore, 100 = -16a + 8a

=> a = - 12.5 m/s2

so, u = 50 m/s

writting a general expression for x,

x = ut + (1/2)at2

x(t) = 50t - 6.25t2.

where initial velocity = u = 50 m/s and acceleration = a = - 12.5 m/s2.

the velocity expression is:

v = dx/dt = 50 - 2(6.25)t = 50 - 12.5t.

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