Units and kinematics
Standard units and basic dimensions
All quantities in mechanics are defined in terms of three fundamental quantities or dimensions: mass, length and time
Force = mass X acceleration. The SI unit is the newton
Strategy
1 Convert units if they're inconsistent and perform any neccessary calculations
2 Check that dimensions have been conserved and that your final answer is in the correct units
Motion in a straight line- definitions and graphs
Position is a vector: the distance and direction from the origin O
Displacement is a vector: the change of position
Distance is a scalar: the magnitude of displacement
Velocity is a vector: the rate of change of displacement
Speed is a scalar: the magnitude of velocity
Average velocity = resultant displacement/ total time
Averge speed = total distance/ total time
The gradient of a displacement-time graph is the velocity
Acceleration is the rate of change of velocity. The gradient of a velocity-time graph is the acceleration
Acceleration = change in velocity/ time = (v-u)/t
The area between the v-t graph and the t-axis is the displacement
Strategy
1 Be clear whether you are being asked for displacement or distance, and velocity or speed
2 Use gradient to calculate velocity from an s-t graph, and acceleration from a v-t graph
3 Use area under a v-t graph to calculate displacement. Keep in mind that area below the t-axis is negative displacement
Eqations of motion for constant acceleration
s = displacement
u = initial velocity
v = final velocity
a = acceleration
t = time
v = u+at
s = 1/2 (u+v)t
s = vt-1/2 at²
v² = u²+2as
Strategy
1 Use the information in the question to list the known values and the variable you need to find. Be careful to distinguish between displacement and distance, and between velocity and speed
2 Choose the correct equation to use
3 Apply the equation to find the numerical value and use it to answer the original question
Motion with varable acceleration
Gradient of s-t graph = velocity at that instant
Gradient of v-t graph = acceleration at that instant
v = ds/dt
a = dv/dt = d²s/dt²
s = ∫v dt and v = ∫a dt
Strategy
1 Identify what dimensions you're dealing with and differentiate or integrate as appropriate
2 Include the constant of integration and calculate its value
3 Use the result of your differentiation or integration to answer the original question