Question

3. A sprinter accelerates at 3.3 m/s? until reaching her top speed of 15 m/s, she then
continues to run at top speed.

a) How long does it take for her to reach top speed?

b) How long does it take her to run the 100 m dash?

Answer 1

(a) The time taken for her to reach the top speed is 4.54 s.

(b) The time taken for her to run the 100 m dash is 7.78 s.

(a) To calculate the time taken to reach the speed, we use the formula below.

Formula:

• a = (v-u)/t.................... Equation 1

Where:

• a = acceleration of the sprinter
• v = final velocity of the sprinter
• u = initial velocity of the sprinter
• t = time

make t the subject of the equation

• t = (v-u)/a................ Equation 2

From the question,

Given:

• v = 15 m/s
• a = 3.3 m/s²
• u = 0 m/s

Substitute these values into equation 2

• t = (15-0)/3.3
• t = 4.54 s.

(b) To calculate the time taken to run the of 100 m dash,  we use the formula below.

Formula:

• S = ut+at²/2...................... Equation 3

From the question,

Given:

• S = 100 m
• u = 0 m/s
• a = 3.3 m/s²

Substitute these values into equation 3

• 100 = 0(t)+3.3t²/2

Solve for t

• 3.3t² = 200
• t² = 200/3.3
• t = √(60.60)
• t = 7.78 s

Hence, (a) The time taken for her to reach the top speed is 4.54 s (b) The time taken for her to run the 100 m dash is 7.78 s

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