Page 51 - Schaum's Outline of Theory and Problems of Applied Physics

36 MOTION IN A STRAIGHT LINE [CHAP. 3

SOLVED PROBLEM 3.11
2
A car has an acceleration of 8 m/s . (a) How much time is needed for it to reach a velocity of 24 m/s if it
starts from rest? (b) How far does it go during this period?
v 24 m/s
(a) t = = = 3s
a 8 m/s 2
(b) Since the car starts from rest, v 0 = 0 and

1
1 2 2 2
s = at = (8 m/s )(3s) = 36 m
2 2
SOLVED PROBLEM 3.12
2
The brakes of a certain car can produce an acceleration of 6 m/s . (a) How long does it take the car to
come to a stop from a velocity of 30 m/s? (b) How far does the car travel during the time the brakes are
applied?
v 30 m/s
(a) t = = = 5s
a 6 m/s 2
(b) Here the signs of v 0 and a are important. The initial velocity of the car is v 0 =+30 m/s and its acceleration is
2
−6 m/s , so
1
1 2 2 2
s = v 0 t + at = (30 m/s)(5s) − (6 m/s )(5s) = 75 m
2 2
SOLVED PROBLEM 3.13
2
A car starts from rest with an acceleration of 2 m/s . What is its velocity after it has gone 200 m?
√
2
v = 2as = (2)(2 m/s )(200 m) = 28 m/s

SOLVED PROBLEM 3.14
An airplane must have a velocity of 50 m/s in order to take off. What must the airplane’s acceleration be
if it is to take off from a runway 500 m long?

2
Since v = 2as,
v 2 (50 m/s) 2 2
a = = = 2.5 m/s
2s (2)(500 m)

SOLVED PROBLEM 3.15
The brakes of a car whose initial velocity is 30 m/s are applied, and the car receives an acceleration of
2
−2 m/s . How far will it have gone (a) when its velocity has decreased to 15 m/s and (b) when it has
come to a stop?
2
2
(a) Since v = v + 2as,
0
2
2
v − v 0 2 (15 m/s) − (30 m/s) 2
s = = = 169 m
2
2a (2)(−2 m/s )
(b) Here v = 0, and so
0 − (30 m/s) 2
s = = 225 m
2
(2)(−2 m/s )