Page 49 - Schaum's Outline of Theory and Problems of Applied Physics

34 MOTION IN A STRAIGHT LINE [CHAP. 3

We can also solve for the time t in terms of v 0 , v, and a:
v − v 0
t =
a
velocity change
Time =
acceleration
Velocity has the dimensions of distance/time. Acceleration has the dimensions of velocity/time or distance/
2
2
time . A typical acceleration unit is the m/s (meter per second squared). Sometimes two different time units are
convenient; for instance, the acceleration of a car that goes from rest to 90 km/h in 10 s might be expressed as
a = 9 (km/h)/s.

SOLVED PROBLEM 3.7
A car starts from rest and reaches a velocity of 40 m/s in 10 s. (a) What is its acceleration? (b)Ifits
acceleration remains the same, what will its velocity be 5 s later?
(a) Here v 0 = 0. Hence
v 40 m/s 2
a = = = 4 m/s
t 10 s
(b)Now v 0 = 40 m/s, so
2
v = v 0 + at = 40 m/s + (4 m/s )(5s) = 40 m/s + 20 m/s = 60 m/s

SOLVED PROBLEM 3.8
A baseball is moving at 25 m/s when it is struck by a bat and moves off in the opposite direction at
35 m/s. If the impact lasted 0.010 s, find the baseball’s acceleration during the impact.
The baseball’s initial velocity is v 0 = 25 m/s and its final velocity is −35 m/s; the minus sign is needed because
the baseball has reversed its direction of motion. Hence
v − v 0 (−35 m/s) − 25 m/s 60 m/s 2
a = = =− =−6000 m/s =−6.0 km/s
t 0.010 s 0.010 s
The acceleration is negative because it is opposite in direction to the original direction of the baseball.

SOLVED PROBLEM 3.9
(a) What is the acceleration of a car that goes from 20 to 30 km/h in 1.5 s? (b) At the same acceleration,
how long will it take the car to go from 30 to 36 km/h?
30 km/h − 20 km/h
v − v 0
(a) a = = = 6.7 (km/h)/s
t 1.5s
v − v 0 36 km/h − 30 km/h
(b) t = = = 0.9s
a 6.7 (km/h)/s

DISTANCE,VELOCITY, AND ACCELERATION
Let us consider a body whose velocity is v 0 when it starts to be accelerated at a constant rate. After time t the
final velocity of the body will be
v = v 0 + at
How far does the body go during the time interval t? The average velocity ¯v of a body whose acceleration
is constant is
v 0 + v
¯ v =
2