1. Carefully sketch x vst. t and v vs. t plots on the axes below for an object w

ID: 2127633 • Letter: 1

Question

1. Carefully sketch x vst. t and v vs. t plots on the axes below for an object which starts with a negative

displacement and a positive velocity, then experiences a negative acceleration and eventually comes to a

stop.

x vx

t t

2. A football player, starting from rest at the line of scrimmage, accelerates along a straight line for 1.5 s.

Then, during a negligible amount of time, he changes the magnitude of his acceleration to a value of 1.1

m/s2

. With this acceleration, he continues in the same direction for another 1.2s. Finally he slows up,

instantly switching his acceleration to 1.7 m/s2 in the opposite of his direction of motion and coming to a

stop after another 2 s.

a. What is the value of his acceleration (assumed to be constant) during the initial 1.5s

period?

b. What is the the total distance covered from start to stop?

using equation v=u+at .... for all the three accelerating motions.....

for 1).

v1=u1 + a*1.5 = a*1.5 .....(u1=0)

for 2)

v2 = v1 + 1.1*1.2

for 3)

0 = v2 + (-1.7)*2

so,

v2 = 3.4 m/s

so,

v1 = v2 - 1.1*1.2 = 3.4-1.1*1.2 = 2.08 m/s

so,

a = v1/1.5 = 2.08/1.5 = 1.3867 m/s^2

using s = ut + 1/2at^2

total distace = s1+s2+s3

s1 = 1/2*1.3867*1.5^2

s2= 2.08*1.2+1/2*1.1*1.2^2

s3 = 3.4*2-1/2*1.7*2^2

so,

total distance = 1/2*1.3867*1.5^2+2.08*1.2+1/2*1.1*1.2^2+3.4*2+1/2*1.7*2^2

= 15.048 m

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