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Mechanics

Velocity against Time Graphs

ODWS Physics: Velocity against Time Graph © David Hoult

a) uniform velocity
b) uniform acceleration

 

ODWS Physics: Velocity against Time Graph © David Hoult

non uniform acceleration

The slope of a v/t graph represents acceleration.

Using a v/t graph to find distance moved

ODWS Physics: using a v/t graph to find distance moved © David Hoult

Uniform velocity:
displacement = v × t = 80m

ODWS Physics: uniform acceleration © David Hoult

Uniform acceleration:
displacement = vav × t
displacement = (15/2) × 6
displacement = 45m

Calculating the magnitude of the displacement of the body is numerically the same as calculating the area under the graph.

Conclusion
The area under a v/t graph represents the magnitude of the displacement of the body.

The Acceleration due to Gravity (Acceleration of Free Fall)

Experiments show that, when air resistance can be ignored, all bodies fall with the same acceleration.

This acceleration is given the symbol g.

g = (about) 9·8 ms-2

The acceleration due to gravity is not exactly the same at all points on the earth’s surface.

Small variations in g are due to:

i) altitude
ii) latitude (the earth is not a sphere).
iii) the rotation of the earth. The value of g is less than it would be if the earth did not rotate. The value of g is reduced most at places where the speed of circular motion is greatest; that is, on the equator.

Velocity against Time Graphs for a Falling Body

a) In vacuum

ODWS Physics: velocity against time for a falling body in a vacuum © David Hoult

 

b) In air

ODWS Physics: velocity against time for a falling body in air © David Hoult

The force of air resistance increases as the velocity of the body increases. Therefore, a body will reach a terminal velocity (vt) when air resistance is equal in magnitude to the weight of the body.

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