An object\'s velocity as a function of time is shown in the plot below. The obje
ID: 1523970 • Letter: A
Question
An object's velocity as a function of time is shown in the plot below. The object begins at position s = 10 m at t = 0 s. What is the object's total displacement at t = 7 s? What is the object's position at t = 7 s? What is the total distance the object Innis moved between t = 0 and t = 7 s. What is the acceleration of this object at t = 1, 3, 5 and 6.5 s? You are in your ear and pushing the gas pedal so that your acceleration is constant. If you travel 250 in between the time when your speedometer reads 40 km/h and 60 km/h how long did it take you to travel that 250 in? What was your acceleration during that time? You throw a ball straight up and measure that it reaches height h and stays in the air for time t. If you want the ball to stay in the air for time 2t. to what maximum height should you throw it? Your initial velocity will be the same for both throws. (NOTE; Yes you can do problems without numbers! Your answer should be in terms of the initial maximum height h. Since the initial velocity is not given - if it had been I would have typed "initial velocity u", h should be the only variable in your answer)Explanation / Answer
3)
a) total displacement = Area under v-t curve
= 1*2 + (1/2)*2*2 +2*3 + (1/2)*2*3 - (1/2)*1*3
= 11.5 m
b) position = 10 + 11.5
= 21.5 m
c)
total distance travelled = 1*2 + (1/2)*2*2 +2*3 + (1/2)*2*3 + (1/2)*1*3
= 14.5 m
d)
at t = 1s,
a = (v2-v1)/(t2-t1) = (3-1)/(2-1) = 2 m/s^2
at t = 3s,
a = (v2-v1)/(t2-t1) = (3-3)/(4-2) = 0 m/s^2
at t = 5s,
a = (v2-v1)/(t2-t1) = (0-3)/(6-4) = -1.5 m/s^2
at t = 6.5 s
a = (v2-v1)/(t2-t1) = (-3 - 0))/(7-6) = -3 m/s^2