Mechanics question (A level maths M1 book, chapter 2, Ex 2A, Q16)

[aurkhan]

Hello can somebody please help me with the second part to this question ? Please show your working. Thank you.

A particle is moving with constant acceleration in a straight line. It passes through three points, A, B, and C with speeds 20ms^-1, 30ms^-1 and 45ms^-1 respectively. The time taken to move from A to B is t1 seconds and the time taken to move from B to C is t2 seconds.

a) show that t1/t2 = 2/3

Given also that the total time taken for the particle to move from A to C is 50 s,
b) find the distance between A and B.

(As per the solutions the answer is 500m but how do you work this out?)

 

[Deleted member 4993]

Hello can somebody please help me with the second part to this question ? Please show your working. Thank you.

A particle is moving with constant acceleration in a straight line. It passes through three points, A, B, and C with speeds 20ms^-1, 30ms^-1 and 45ms^-1 respectively. The time taken to move from A to B is t1 seconds and the time taken to move from B to C is t2 seconds.

a) show that t1/t2 = 2/3

Given also that the total time taken for the particle to move from A to C is 50 s,
b) find the distance between A and B.

(As per the solutions the answer is 500m but how do you work this out?)

The time to travel from A to C = 50 s = 2.5 * t₁ (Why?) → t₁ = 20 s → acceleration = (30 - 20)/20 = 0.5 m/s²

Galileo's third equation:

v² = u² + 2*a*s

where:

v = final velocity

u = initial velocity

a = acceleration

s = distance travelled

solve it (or you can use v-t curve and the area under the curve)

 

[JeffM]

Hello can somebody please help me with the second part to this question ? Please show your working. Thank you.

A particle is moving with constant acceleration in a straight line. It passes through three points, A, B, and C with speeds 20ms^-1, 30ms^-1 and 45ms^-1 respectively. The time taken to move from A to B is t1 seconds and the time taken to move from B to C is t2 seconds.

a) show that t1/t2 = 2/3

Given also that the total time taken for the particle to move from A to C is 50 s,
b) find the distance between A and B.

(As per the solutions the answer is 500m but how do you work this out?)

F = acceleration (in meters per second squared)

v = velocity (in meters per second)

t = time (in seconds)

d = distance (in meters)

\(\displaystyle \int F * dt = Ft + G = v,\) right?

\(\displaystyle \int v * dt = \int(Ft + G)dt = \dfrac{Ft^2}{2} + Gt + H = d,\) right?

F, G, and H are constants. What information do you have to determine the values of the constants?

Hint 1 When you start measuring time is arbitrary so let's say t = 0 when the particle is at point A.

Hint 2 What is the meaning of the sum t₁ + t₂.