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Question
Solve the following problem.
A car moves in a circle at a constant speed of 50 m/s and completes one revolution in 40 s. Determine the magnitude of the acceleration of the car.
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Solution 1
Given: v = 50 m/s, t = 40 s, s = 2πr
To find: acceleration (a)
Formulae:
i. v = `"s"/"t"`
ii. a = `"v"^2/"r"`
Calculation: From formula (i),
`50 = (2pi"r")/40`
∴ r = `(50 xx 40)/(2pi)`
∴ r = `1000/pi` cm
From formula (ii),
a = `"v"^2/"r" = 50^2/(1000//pi)`
a = `(5pi)/2 = 7.85 "m"//"s"^2`
The magnitude of acceleration of the car is 7.85 m/s2.
Solution 2
Given: v = 50 m/s, t = 40 s,
To find: acceleration (a)
Formula: a = rω2 = vω
Calculation: From formula,
a = vω
`= "v"(("2"pi)/"t")`
`= 50((2 xx 3.142)/40)`
`= 5/2 xx 3.142`
∴ a = 7.85 m/s2
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