18 pdf a) A car starts from rest, and then begins driving with a constant accele

Question

18 pdf a) A car starts from rest, and then begins driving with a constant acceleration of 4.0 m/s2 south for 2.0 seconds. What is the car's velocity at the end of this acceleration, written in tems of components (in the usual cordinates)? b) A ball rolls straight down a ramp, starting from rest, and taking 0.73 s to reach the bottom. The ramp is 2.0 ft tall, and 5.0 ft wide horizontally. The ball's speed at the bottom of the hill is 8.0 ft/s. What was the magnitude and direction of the ball's average acceleration? Initial

Explanation / Answer

a)

car's velocity at the end of 2 sec is V = Vo+(a*t)

Vo is the initial velocity = 0 m/sec

a = 4 m/s^2

t = 2 sec

then V = Vo+(a*t) = 0 + (4*2) = 8 m/sec

consider south as negatice y-axis

then interms of coordinates

(0,-8) m/s

b) sin(theta) = h/sqrt(h^2+w^2) = 2/sqrt(2^2+5^2) = 0.371

time taken is t = 0.73 sec

v = 8 ft/sec

initial speed is Vo = 0 ft/sec

using kinematic equations

V = Vo + (a*t)

8 = (0)+(a*0.73)

a = 8/0.73 = 10.95 ft/s^2 direction is along the down the inclined plane

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