DATA A model car starts from rest and travels in a straight line. A smartphone mounted on the car has an app that transmits the magnitude of the car’s acceleration (measured by an accelerometer) every second. The results are given in the table. Time (s) Acceleration ( m/s 2 ) 0 5.95 1.00 5.52 2.00 5.08 3.00 4.55 4.00 3.96 5.00 3.40 Each measured value has some experimental error, (a) Plot acceleration versus time and find the equation for the straight line that gives the best fit to the data, (b) Use the equation for a ( t ) that you found in part (a) to calculate υ ( t ), the speed of the car as a function of time. Sketch the graph of υ versus t . Is this graph a straight line? (c) Use your result from part (b) to calculate the speed of the car at t = 5.00 s. (d) Calculate the distance the car travels between t = 0 and t = 5.00 s.
DATA A model car starts from rest and travels in a straight line. A smartphone mounted on the car has an app that transmits the magnitude of the car’s acceleration (measured by an accelerometer) every second. The results are given in the table. Time (s) Acceleration ( m/s 2 ) 0 5.95 1.00 5.52 2.00 5.08 3.00 4.55 4.00 3.96 5.00 3.40 Each measured value has some experimental error, (a) Plot acceleration versus time and find the equation for the straight line that gives the best fit to the data, (b) Use the equation for a ( t ) that you found in part (a) to calculate υ ( t ), the speed of the car as a function of time. Sketch the graph of υ versus t . Is this graph a straight line? (c) Use your result from part (b) to calculate the speed of the car at t = 5.00 s. (d) Calculate the distance the car travels between t = 0 and t = 5.00 s.
DATA A model car starts from rest and travels in a straight line. A smartphone mounted on the car has an app that transmits the magnitude of the car’s acceleration (measured by an accelerometer) every second. The results are given in the table.
Time (s)
Acceleration ( m/s2)
0
5.95
1.00
5.52
2.00
5.08
3.00
4.55
4.00
3.96
5.00
3.40
Each measured value has some experimental error, (a) Plot acceleration versus time and find the equation for the straight line that gives the best fit to the data, (b) Use the equation for a(t) that you found in part (a) to calculate υ(t), the speed of the car as a function of time. Sketch the graph of υ versus t. Is this graph a straight line? (c) Use your result from part (b) to calculate the speed of the car at t = 5.00 s. (d) Calculate the distance the car travels between t = 0 and t = 5.00 s.
An object starts at the origin with an initial velocity of v0 = 10.0 m/s i + 15.0 m/s j. The object is given a constant acceleration of a = 1.00 m/s2 i + 2.00 m/s2 j. (a) Calculate the (x,y) position of the object at t = 10.0 seconds. (b) Calculate the velocity of the object (vx,vy) at t = 10.0 seconds.
A car starts from rest, then accelerates at a constant rate over a distance of 89 m. It then immediately decelerates at a constant rate over a distance of 152 m. The entire trip lasts a total duration of 27.2 s. What were the magnitudes of the car s accelerations for the speedup and slowdown stages respectively?
1. 1.76 m/s^2, then 1.03 m/s^2
2. 3.27 m/s^2, then 5.59 m/s^2
3. 0.65 m/s^2, then 0.65 m/s^2
4. 5.59 m/s^2, then 3.27 m/s^2
On a one lane road, a person driving a car at v1 = 58 mi/h suddenly notices a truck 1.1 mi in front of him. That truck is moving in the same direction at v2 = 35 mi/h. In order to avoid a collision, the person has to reduce the speed of his car to v2 during time interval Δt. The smallest magnitude of acceleration required for the car to avoid a collision is a. During this problem, assume the direction of motion of the car is the positive direction.
1. Use the expressions you entered in parts (c) and (f) and enter an expression for a in terms of d, v1, and v2.
a = ( v2 - v1 )/Δt
Δt = ( 2 ) ( d )/( v1 - v2 )
2. Calculate the value of a in meters per second squared.
Chapter 2 Solutions
University Physics, Volume 2 (Chs. 21-37) (14th Edition)
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