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Mass \( m = 10 \, \text{kg} \), gravitational acceleration \( g = 9.8 \, \text{m/s}^2 \), angle \( \theta = 30^\circ \).
Gravitational force component: \( 10 \times 9.8 \times \sin(30^\circ) = 98 \times 0.5 = 49 \, \text{N} \).
Net force \( F_{\text{net}} = 50 \, \text{N} - 49 \, \text{N} = 1 \, \text{N} \).
Using \( F = ma \), solve for \( a \): \( a = F_{\text{net}}/m = 1/10 = 0.1 \, \text{m/s}^2 \).
#### 0.1 m/s²
Find the sum of the series \( 1 + 3 + 5 + \dots + 99 \).
This is an arithmetic series of odd numbers with first term \( a = 1 \), common difference \( d = 2 \), and last term \( l = 99 \).
Number of terms \( n \): \( l = a + (n-1)d \rightarrow 99 = 1 + (n-1) \times 2 \).
Solve: \( 98 = 2(n-1) \rightarrow n-1 = 49 \rightarrow n = 50 \).
Sum of arithmetic series: \( S = \frac{n}{2}(a + l) \).
