Motion in a Straight Line Quiz

Motion in a Straight Line

• Motion of objects is described using motion graphs and numerical values. This is crucial for vehicle design, enabling faster and more efficient vehicles.
• Distance-time graphs can represent an object's movement along a straight line. The gradient of the line on a distance-time graph represents speed. A steeper line indicates faster movement.
• Calculating speed from a distance-time graph involves determining the gradient.
• Velocity-time graphs can also represent motion along a straight line. The gradient of the line on a velocity-time graph represents acceleration.

Velocity, Acceleration, and Distance

• Distance: Numerical description of how far apart two things are (e.g., Edinburgh to Glasgow is ~50 miles). It's scalar (only size matters).
• Speed: Rate of change of distance (distance travelled per unit time). Also scalar.
• Speed Variation: Speed changes when walking, running, or driving (i.e., speeding up, slowing down, stopping). Wind and sound speeds are also variable, depending on different factors.
• Speed Calculation (Constant Speed): Distance travelled = Speed x Time
• Average Speed Calculation (Variable Speed): Total distance traveled / total time taken.
• Velocity: Speed in a particular direction. A vector quantity (magnitude and direction). Calculated using displacement, not distance.
• Displacement: Distance from the starting point in a straight line with a specified direction (e.g., 50 km due north).
• Acceleration: Rate of change of velocity. Calculated as change in velocity divided by time taken. Measured in metres per second squared (m/s²).
• Deceleration: Slowing down; negative acceleration.
• Acceleration Calculation: Acceleration = change of velocity ÷ time taken
• Calculating Speed from a Distance-Time Graph: For constant speed, the gradient is the speed. For changing speed (acceleration or deceleration), a tangent to the curve at a specific time gives the instantaneous speed at that point. The tangent's gradient is the instantaneous speed.
• Calculating Acceleration from a Velocity-Time Graph: The gradient of a velocity-time graph represents acceleration.
• Calculating Displacement from a Velocity-Time Graph: The area under a velocity-time graph represents the total displacement.
• Equations of Motion (Constant Acceleration):
• v² = u² + 2as (where v = final velocity, u = initial velocity, a = acceleration, s = displacement)
• Example Calculations:
• Example 1 (dropping biscuit): A biscuit is dropped 300 m (s = 300 m), from rest (u = 0 m/s), from the Eiffel tower. Calculate its final velocity (v). (Acceleration due to gravity = 9.8 m/s²).
• v² = 0² + 2 * 9.8 m/s² * 300 m
• v² = 5880 m²/s²
• v = √5880 m²/s² ≈ 76.7 m/s
• Example 2 (accelerating train): A train accelerates uniformly from rest (u = 0 m/s) to 24 m/s (v = 24 m/s) on a straight part of the track. It travels 1,440 m (s = 1,440 m). Calculate its acceleration (a).
• v² = u² + 2as
• 24² = 0² + 2 * a * 1400
• 576 = 2800a
• a = 576 / 2880 ≈ 0.20 m/s²
• Velocity Changes: Objects in circular motion are accelerating because their direction is constantly changing, despite potentially a constant speed. Velocity (a vector quantity) changes if either its magnitude or direction changes.