
The acceleration of a moving object depends on two factors:
 the amount the object’s speed changes (Δv) and
 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.

What 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/s^{2} 

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
$$\text{\Delta}v=a\text{\Delta}t$$
What is the speed of an object that starts from rest and accelerates at a constant 2 m/s^{2} for 10 s?
Asked: 
final speed v 
Given: 
acceleration a = 2 m/s^{2}, time interval of Δt = 10 s,
and initial speed v_{0} = 0 (from rest) 
Relationships: 
a = Δv/Δt → Δv = aΔt

Solution: 
We use the change in speed Δv = v − v_{0} to rewrite the equation as
v − v_{0} = aΔt → v = v_{0} + aΔt
Then we calculate the final speed
v = 0 + (2 m/s^{2} × 10 s) = 20 m/s 


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 straightline graph with a slope of 0.5 m/s^{2}.
