Chapter 2: Accelerated motion
2 Equation 1 can be deduced from the definition of acceleration. a Acceleration can be defined as:
(final velocity − initial velocity ) time Write this equation in symbols. b Rearrange the equation to give the first of the equations of motion. c Which of the five quantities from question 1 is not involved in this equation? 3 Equation 2 can be found by imagining that an object moves at a constant velocity equal to its average velocity. a Write an equation (in words and then in symbols) for the object’s average velocity, in terms of its initial and final velocities. b Use your answer to part a to write down the equation for displacement. To find the object’s displacement, multiply the average velocity by the time taken. c Which of the five quantities from question 1 is not involved in this equation? 4 To deduce the equations 3 and 4, we start from a simple velocity–time graph:
v
Velocity / m s−1
9
u
0
t
0 Time / s
a Describe the motion represented by this graph. We have to deduce an equation for displacement. This is represented by the area under the graph. We can divide this area into two parts: displacement = area of rectangle + area of triangle TIP Equation 1 defines acceleration.
b The area of the rectangle represents the displacement if the object had moved at a steady speed u for time t. What is the value of this area? c The area of the triangle represents the object’s additional displacement resulting from its acceleration. The height of this triangle is v – u. Rearrange the equation that defines acceleration to find the height of the triangle in terms of a and t.