Determining acceleration

The acceleration of a moving object depends on two factors:
  1. the amount the object’s speed changes (Δv) and
  2. the time over which the change occurs (Δt).
Unless it is otherwise stated, you should assume that the acceleration in a physics problem is constant. Thus the speed changes by the same amount every second. Read the text aloud
Start and finish conditions for a cart rolling down a hillWhat is the acceleration of a cart that rolls down a hill if it starts at rest and reaches a speed of 1.2 m/s after 0.6 s?

Asked: acceleration a
Given: change in speed of Δv = 1.2 m/s, interval of time Δt = 0.6 s
Relationships:  a = Δv/Δt
Solution: a = 1.2 m/s ÷ 0.6 s = 2 m/s2
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Another type of problem asks for the speed of an object given the acceleration and time. The change in speed Δv for an accelerated object is Δv=aΔt What is the speed of an object that starts from rest and accelerates at a constant 2 m/s2 for 10 s?
Asked: final speed v
Given: acceleration a = 2 m/s2, time interval of Δt = 10 s,
and initial speed v0 = 0 (from rest)
Relationships: a = Δvt → Δv = aΔt
Solution: We use the change in speed Δv = v − v0 to rewrite the equation as
vv0 = aΔtv = v0 + aΔt
Then we calculate the final speed
v =  0 + (2 m/s2 × 10 s) = 20 m/s
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ErgoBot rolling down a ramp
Acceleration causes a nonzero slope on the velocity versus time graph, because acceleration represents change in velocity over time. Mathematically, the slope of a v vs. t graph is the change in velocity divided by the change in time, which is the definition of acceleration. In the example above, velocity increases at a steady rate of 0.5 m/s each second, producing a straight-line graph with a slope of 0.5 m/s2. Read the text aloud

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