Which graph represents the motion of a car that is travelling along a straight road with a speed that increases uniformly with time?

Question 3

Which graph represents the motion of a car that is travelling along a straight road with a speed that increases uniformly with time?

Reference: Past Exam Paper – November 2008 Paper 1 Q8

Solution:

Answer: A. 

We need to look at the axes carefully in each graph so that we can know which quantities are involved and which other quantities may be obtained from the gradient or area under graph.

‘Travelling along a straight road with a speed that increases uniformly with time’ means that there is a uniform acceleration (that is, the acceleration is constant; the acceleration is not changing).

Graph A: Acceleration-time graph – acceleration has a constant value

Graph B: Acceleration-time graph – acceleration is increasing from a non-zero value

Graph C: Displacement-time graph – straight line with a positive gradient à gradient is constant à velocity is constant

Graph D: Displacement-time graph – horizontal line à gradient = 0 à velocity = 0

A constant force pushes a block along a horizontal frictionless surface. The block moves from rest through a fixed distance.

Question 1

A constant force pushes a block along a horizontal frictionless surface. The block moves from rest through a fixed distance.

What is the relationship between the final speed v of the block and its mass m?

Reference: Past Exam Paper – June 2017 Paper 13 Q16

Solution:

Answer: C.

v² = u² + 2as

Since the block moves from rest, u = 0.

v² = 2as

So, v² ∝ a

Since a constant force is applied, F = ma, giving a = F/m

So, acceleration a ∝ 1/m

Replacing the relationship a ∝ 1/m into the equation involving velocity,

v² ∝ 1 / m

v ∝ 1 / √m

Variables x and y are related by the equation y = p – qx where p and q are constants.

Question 2

Variables x and y are related by the equation y = p – qx where p and q are constants.

Values of x and y are measured experimentally. The results contain a systematic error.

Which graph best represents these results?

Reference: Past Exam Paper – November 2012 Paper 12 Q6

Solution:

Answer: A.

Equation: y = p – qx  

Comparing with the equation of a line y = mx + c, the gradient is negative and constant (m = -q). So, it is a straight line. [C and D incorrect]

Systematic error is due to the instrument, so all points should lie on the line as the error always occurs in the same direction.

From the equation, when x = 0, y = p, but due to systematic error, this value is reduced.

Choice A is correct as it shows no random error but a systematic error with the line not going through p.

Choice B shows random error without systematic error.