Acceleration Problems
READ
Acceleration is the rate of change in the speed of an object. To determine the rate of acceleration, you use the formula below. The units for acceleration are meters per second per second or m/sec2.
text(Acceleration) = (text(Final speed) - text(Beginning speed))/text(Time)
a = (v_2 - v_1)/t
A positive value for acceleration refers to the rate of speeding up, and negative value for acceleration refers to the rate of slowing down. The rate of slowing down is also called deceleration.
The acceleration formula can be rearranged to solve for other variables such as final speed (v2) and time (t).
v_2 = v_1 + (a * t)
t = (v_2 -v_1)/a
EXAMPLES
A skater increases her velocity from 2.0 m/sec to 10.0 m/sec in 3.0 seconds. What is the skater's acceleration?
Looking for
Acceleration of the skater.
Given
Beginning speed = 2.0 m/sec
Final speed = 10.0 m/sec
Change in time = 3 seconds
Relationship
a = (v_2 - v_1)/t
Solution
text(Acceleration) = ((10.0 text( m/sec)) - (2.0 text( m/sec)))/(3 text( sec))
text(Acceleration) = ((8.0 text( m/sec)))/(3 text( sec))
text(Acceleration) = 2.7 text( m/)(text(sec)^2)
The acceleration of the skater is 2.7 meters per second per second.
A car accelerates at a rate of 3.0 m/sec2. If its original speed is 8.0 m/sec, how many seconds will it take the car to reach a final speed of 25.0 m/sec?
Looking for
The time to reach the final speed.
Given
Beginning speed = 8.0 m/sec
Final speed = 25.0 m/sec
Acceleration = 3.0 m/sec
Relationship
t = (v_2 - v_1)/a
Solution
text(Time) = (25.0 text( m/sec) - 8.0 text( m/sec))/(3.0 text( m/sec)^2)
text(Time) = (17.0 text( m/sec))/(3.0 text( m/sec)^2) = 5.7 text( sec)
The time for the car to reach it is 5.7 seconds.
PRACTICE (a) While traveling along a highway a driver slows from 46 m/sec to 40 m/sec in 46 seconds. What is the automobile's acceleration? (Remember that a negative value indicates a slowing down or deceleration.)
Looking for
The automobile's
Given
Beginning speed =
m/sec
Final speed =
m/sec
What is the final given quantity?
=
in units of
Relationship
(Please use vi and vf.)
a =
Solution
(Please give the quantity that you are looking for, in words, in the first answer field and the remaining quantities in numbers with appropriate units; ex. 10 m/sec. Add leading zeros for decimal answers and use '^' for exponents. Round decimals to two decimal places.)
= (
-
)/
=
(b) A parachute on a racing dragster opens and changes the speed of the car from 80 m/sec to 33 m/sec in a period of 4 seconds. What is the acceleration of the dragster?
m/sec2
(c) The cheetah, which is the fastest land mammal, can accelerate from 0.0 mi/hr to 70.0 mi/hr in 3.0 seconds. What is the acceleration of the cheetah? Give your answer in units of mph/sec.
mph/sec
(d) The Lamborghini Diablo sports car can accelerate from 0.0 km/hr to 99.2 km/hr in 4.0 seconds. What is the acceleration of this car? Give your answer in units of kilometers per hour/sec.
km/h/sec
(e) Which has greater acceleration, the cheetah or the Lamborghini Diablo? (To figure this out, you must remember that there are 1.6 kilometers in 1 mile.)
Cheetah
Lamborghini
(f) The table below includes data for a ball rolling down a hill. Fill in the missing data values in the table and determine the acceleration of the rolling ball.
Time (seconds) Speed (km/h)
0 (start) 0 (start)
2 3
6
9
8
10 15
Acceleration
km/h/sec
(g) A car traveling at a speed of 35 m/sec encounters an emergency and comes to a complete stop. How much time will it take for the car to stop if its rate of deceleration is -4.1 m/sec2?
seconds
(h) If a car can go from 2.3 to 54 mi/hr in 8.07 seconds, what would be its final speed after 5.07 seconds if its starting speed were 48 mi/hr?
mi/hr
(i) A cart rolling down an incline for 4.7 seconds has an acceleration of 3.1 m/sec2. If the cart has a beginning speed of 0.8 m/sec, what is its final speed?
m/sec
(j) A helicopter's speed increases from 23.9 m/sec to 58.5 m/sec in 5.07 seconds. What is the acceleration of this helicopter?
m/sec2
(k) Below are three situations. In which is the acceleration most similar to the helicopter's in question (j)?
I. An object going from 0 m/sec to 25 m/sec in 5 seconds.
II. An object going from 0 m/sec to 7 m/sec in 2 seconds.
III. An object going from 5 km/h to 30 km/h in 1 second.
The acceleration is most similar to which of the following.
I
II
III
