Questions: An object starts from rest and undergoes uniform acceleration. During the first second it travels 5.0 m . How far will it travel during the third second?

Solution Steps

• The object starts from rest, so initial velocity \( u = 0 \).
• Distance traveled in the first second \( s_1 = 5.0 \, \text{m} \).
• Using the equation \( s = ut + \frac{1}{2}at^2 \), where \( t = 1 \) second: \[ 5.0 = 0 \cdot 1 + \frac{1}{2}a \cdot 1^2 \] \[ 5.0 = \frac{1}{2}a \] \[ a = 10 \, \text{m/s}^2 \]

• Using the same equation \( s = ut + \frac{1}{2}at^2 \) for \( t = 3 \) seconds: \[ s_3 = 0 \cdot 3 + \frac{1}{2} \cdot 10 \cdot 3^2 \] \[ s_3 = \frac{1}{2} \cdot 10 \cdot 9 \] \[ s_3 = 45 \, \text{m} \]

• Distance traveled in the first 2 seconds \( s_2 \): \[ s_2 = 0 \cdot 2 + \frac{1}{2} \cdot 10 \cdot 2^2 \] \[ s_2 = \frac{1}{2} \cdot 10 \cdot 4 \] \[ s_2 = 20 \, \text{m} \]
• Distance traveled during the third second: \[ s_{\text{third}} = s_3 - s_2 \] \[ s_{\text{third}} = 45 \, \text{m} - 20 \, \text{m} \] \[ s_{\text{third}} = 25 \, \text{m} \]

Final Answer