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The head of a rattlesnake can accelerate 50 m1s 2 in striking a victim. If a car could do as well, how long would it take for it to reach a speed of 100 km/h from rest?

The head of a rattlesnake can accelerate 50 m1s2 in striking a victim. If a car could do as well, how long would it take for it to reach a speed of 100 km/h from rest?

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
We assume that the motion is along the x direction only.
Given:
Acceleration of rattlesnake, ax = 50 m/s2.
Initial speed of car, v0x = 0 km/h.
Final speed of car, vx = 100 km/h.
Given that the acceleration of the car is equal to the acceleration of the rattlesnake, the time (say t) taken by the car to reach the final speed vx is given as:

232-1887_7.PNG
If the acceleration of the car is constant, the magnitude of distance (say x) travelled by the car is given as:
With initial condition x0 = 0, x is given as:
232-1707_8.PNG
Substitute the given values to obtain the value of x as:
232-1503_9.PNG
Rounding off to two significant figures
x = 7.5 m
Therefore the car will travel 7.5 m to reach the final speed of 100 km/ h if the acceleration of the car is equal to the acceleration of the rattlesnake.

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