Using the following data, draw a velocity-time graph for a short journey on a straight road on a motorcycle.


Use the graph to calculate:
 (a) The initial acceleration
 (b) The final acceleration
 (c) The total distance traveled by the motorcyclist.

[Ans: (a) 0.33 m s⁻², (b) -0.67 m s⁻², (c) 2.7 km ]


Solution:

According to the given data, the graph will be as below:



(a) The Initial Acceleration:

From the graph
Initial Acceleration = Slope of the line OA = `\frac {AE}{OE}`

Initial Acceleration =  `\frac {20 ms^{-1}}{60s}` = 0.33 m s⁻² --------------Ans (a)

(b) The Final Acceleration:

From the graph
Final Acceleration = Slope of the line BC = `\frac {BC}{DC}`

Final Acceleration =  `\frac {-20 ms^{-1}}{30s}` = -0.67 m s⁻² --------------Ans (b)

(c) Total Distance Traveled:

S = S₁ + S₂ + S₃

S = Area of 🛆OAE + Area of ㅁEABD + Area of 🛆BCD  

S = `\frac {1}{2}`vt₁ + vt₂ + `\frac {1}{2}`vt₃

S = `\frac {1}{2}`(20 x 60) m+ (20 x 90) m + `\frac {1}{2}`(20 x 30) m

S = 600 m + 1800 m + 300 m

S = 2700 m

or

S = 2.7 km  --------------- Ans (c)



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