Displacement-Time and Velocity Time Graphs

Question 1

what would the line from a displacement time graph look like for an object moving at constant velocity look like

Answer 1

• a straight line
• with a positive gradient
• starting from 0,0 usually

Question 2

what does the gradient of the line indicate

Answer 2

the velocity

Question 3

why does the gradient indicate the velocity

Answer 3

• because the gradient is calculated by the change in y over the change in x
• the y axis is displacement and the x axis is time
• so it would be the change in displacement over the change in time
• and velocity = displacement / time

Question 4

what would the line from a displacement time graph look like for an object accelerating down a ramp

Answer 4

• the line would be an inwards curve getting steeper

- usually starting from 0,0

Question 5

why does the line indicate that the object is accelerating

Answer 5

• because the line is showing an increasing change in velocity
• which is the definition of acceleration

Question 6

how would you calculate the instantaneous velocity of the object

Answer 6

• by drawing a tangent from a point on the line
• and calculating the gradient of that line
• by dividing the change in d over the change in t

Question 7

why would drawing a triangle off of the curved line to calculate the velocity be less effective

Answer 7

• for starters it would only be relatively accurate if your drawn triangle and your d and t values were very small
• but even with these values the calculation would be difficult
• and would lead to large uncertainties in the calculated velocity

Question 8

if you drew a velocity time graph with there being a constant velocity, how would you calculate the distance traveled

Answer 8

• by finding the area under the line
• with a constant velocity the line would just be horizontal
• so it would be done with total time x velocity

Question 9

how would you find the distance traveled in a velocity time graph if your straight line had a positive gradient

Answer 9

• by finding the ares under the line
• the distance between the bottom of the line and the top are the initial and final velocities
• which can be shown as v + u
• you would then times that by time to give t(v + u)
• but because the positive gradient makes the area under the line a triangle, you divide it by 2
• to get t(v + u) / 2

Question 10

what is the formula for calculating the straight line with a positive gradient from

Answer 10

• the suvat equations

- s = t(v + u) / 2

Question 11

what would a straight line with a positive gradient on a velocity time graph indicate

Answer 11

• an increasing change in velocity

- so acceleration

Question 12

what would an inwards curved line getting steeper with a positive gradient on a velocity time graph indicate

Answer 12

• an increasing change of the increasing change in velocity

- so just an increasing acceleration

Question 13

what is the worded formula for acceleration

Answer 13

change in velocity / change in time

Question 14

what would a negative gradient on a velocity time graph indicate

Answer 14

• that the object is slowing down

- or decelerating