chapter 10
Define acceleration and state the SI units for acceleration.
Acceleration is the rate at which velocity changes over time. An object accelerates if its speed,direction, or both change. The formula for acceleration is a = (vf - vi) / t. The SI units for acceleration are meters per second squared, m/s2
What is the SI unit for speed?
Meters per second, m/s
Define speed and velocity and compare and contrast the two.
Speed is the distance traveled divided by the time interval during the motion occurred. Speed is a scalar quantity, defined only by magnitude. Velocity is the speed of an object in a particular direction. Velocity can also be defined as displacement divided by time. Velocity is a vector quantity, including magnitude and direction. Both speed and velocity have the SI unit of meters per second.
Calculate the displacement in meters a cyclist would travel in 5.00 h at an average velocity of 12.0 km/h to the southwest.
d = vt = (12 km/h)(5 h) = 60 km = 60 000 m to the southwest
Marisa's car accelerates at an average rate of 2.6 m/s2 Calculate how long it takes her car to speed up from 24.6 m/s to 26.8 m/s.
t = (vf - vi) / a = (26.8m/s - 24.6m/s) / 2.6 m/s2 = 0.85 s
Find the velocity of a swimmer who swims 110 m toward the shore in 72 seconds.
v = d / t = 110m / 72s = 1.5 m/s toward shore
A wheelchair racer finishes a 132 m race in 18 seconds. What is the racer's average speed
v = d / t = 132m / 18s = 7.3 m/s
A cyclist travels at a constant velocity of 4.5 m/s westward, and then speeds up with a steady acceleration of 2.3 m/s2. Calculate the cyclist's speed after accelerating for 5.0 s.
vf = vi +at = 4.5m/s + (2.3m/s2)(5s) = 16 m/s
Is an object moving in a circle at a constant speed accelerating? Why or why not?
Yes, an object moving in a circle at a constant speed is accelerating because it is changing direction. Acceleration refers to a change in velocity, which could be a change in magnitude (speed) or direction. Traveling in a circle requires a continuous change in direction.
Explain how you can find acceleration from a velocity-time graph.
Acceleration is the slope of a velocity-time graph. The reason is that the slope of any line is change in y over change in x. Since the velocity is on the y-axis and the time is on the x-axis, this directly comes from the equation for acceleration, a = (vf - vi) / t.
Define distance and displacement and compare and contrast the two. Give an example of when you would use each one.
Distance is the length of the path traveled. Distance is a scalar quantity, meaning that it is fully described by magnitude. Distance would be used when a GPS in a car calculates how far a destination is away from your current location. Displacement is the change in positon of an object. Displacement is a vector quantity meaning that it includes magnitude and direction. Displacement would be used when considering the path a bird takes to fly to a destination. Both distance and displacement have the SI unit of meters.