(f) A motorbike accelerates from \( 12 \mathrm{~m} \mathrm{~s}^{-1} \) to \( 36 \mathrm{~m} \mathrm{~s}^{-1} \) in 3 seconds. Calculate the acceleration of the motorbike. Calculation

To calculate the acceleration of the motorbike, you can use the formula for acceleration: \[ \text{Acceleration} (a) = \frac{\text{Final velocity} (v) - \text{Initial velocity} (u)}{\text{Time} (t)} \] Plugging in the values: - \( v = 36 \, \mathrm{m/s} \) - \( u = 12 \, \mathrm{m/s} \) - \( t = 3 \, \mathrm{s} \) \[ a = \frac{36 \, \mathrm{m/s} - 12 \, \mathrm{m/s}}{3 \, \mathrm{s}} = \frac{24 \, \mathrm{m/s}}{3 \, \mathrm{s}} = 8 \, \mathrm{m/s}^2 \] So, the acceleration of the motorbike is \( 8 \, \mathrm{m/s}^2 \). Did you know that the concept of acceleration dates back to the time of Galileo in the 16th century? He famously studied the motion of objects by rolling balls down inclined planes, laying down the foundations that would eventually lead to Newton's laws of motion. Isn't it fascinating how centuries ago they were already unraveling the secrets of movement? Acceleration isn’t just a math concept; it's also crucial in real-world applications! For instance, engineers must calculate acceleration when designing amusement park rides. If a roller coaster accelerates too quickly, it can be uncomfortable or even unsafe for riders. That’s why balance and safety considerations are pivotal when devising thrilling experiences!