Rectilinear motion

• Rectilinear motion means motion along a straight path
• Average velocity is the velocity of an object over a specified time frame. Average velocity = Displacement/time
• Instantaneous velocity is the velocity of an object at a specific point in time. It can be found from a displacement-time graph by drawing a tangent to the graph at the specific time and calculating the gradient
• Acceleration is the rate of change of velocity. It is calculated using the formula: a = v-u/t and measurements are ms^-2
• For uniform acceleration, to measure average and instantaneous velocity, the acceleration is calculated through a = (v-u)/t
• Velocity and acceleration are vectors. If an object slows down, (v-u) will be negative. This means that acceleration is in the opposite direction to the velocities and the object has a negative value of acceleration
• The motion of an object moving at constant velocity or accelerating uniformly can be described by the set of equations known as the equations of motion. s = displacement (m), u = initial velocity (ms^-1) at t = 0s, v = final velocity (ms^-1), a = acceleration (ms^-2) and t = time (s)
• The first equation of motion is: v = u + at
• The second equation of motion is: s = (u + v)/2 x t
• The third equation of motion is: s = ut + 1/2at^2
• The fourth equation of motion is: v^2 = u^2 + 2as
• The acceleration of free fall on Earth commonly termed the acceleration due to gravity, g has a value of 9.8ms^-2
• The horizontal distance travelled by projectiles can be found by considering the vertical and horizontal motions separately. In the vertical plane, the object will accelerate down at 9.8ms^-2, while the horizontal velocity remains constant (in the assumed absence of air resistance). The equations of motion can be applied to the vertical motion to ascertain the time spent by the object in free fall, then the horizontal displacement is the product of the constant horizontal velocity and this time.
• If an object is projected at an angle, the vertical and horizontal motion can still be treated separately by considering the components of the velocity in each plane. In the vertical plane, the initial velocity is usinθ (upwards) and the acceleration is 9.8ms^-2 (downwards). As both are vectors, if a positive value is assigned to the initial velocity, the acceleration and the downward velocities and displacements will have negative values. Neglecting air resistance, the horizontal component of the initial velocity ucosθ, will remain constant throughout the motion
• Displacement-time graphs show change in displacement over time, and so their gradient represents the velocity.

  
• Velocity-time graphs through the gradient of the displacement-time graph being taken for a range of times and plotted forming a velocity-time graph
• The acceleration of an object is therefore equal to the gradient of a velocity-time graph. If the object is slowing down, the gradient will be negative. A negative value of acceleration indicates that the vector has the opposite direction to the velocity